7. If, for all real numbers x, f'(x) < 0 and f"(x) > 0, which of the following curves could be a part of the graph of f?

Q: 30. Consider the function defined by 0ifx 1 Sketch this graph and find all points where the graph is…

A:

Q: 1 Is the function given by f(x)= 3x+2, for x ≤ 3, 4x-7, for x>3, continuous at x = 3? Why or why…

A:

Q: Find the equation of the tangent line to the graph of the function at the given value of x. f(x) =…

A: Given f(x) = x2 + 5x

Q: Suppose that the tangent line to the graph of a function f at x=2 passes through the point (5,19)…

A: Given that the tangent line to the graph of a function f at x=2 passes through the point (5,19) and…

Q: Find an equation of the tangent line to the graph of f(x)

A: Given function ,         fx=3-Yxx+5at -1,1To find the slope , we differenntiate the function fx…

Q: Find the length of the curve of the graph of the indicated function. y = In(sen x), between points…

A:

Q: Find an equation of the tangent line to the graph of f(x) f(x) = 1/√5x at x = 9.

A: Given equation of curve

Q: 3. If y = 2 – 1, find the length of the graph of f from point z = 0 to a = 1.

A: Here, the given function is: y=f(x)=423x-1 To find the length of the curve from x=0 to x=1

Q: 9. What is the equation of the line tangent to the graph of the function f at the point (1,1)? f (x)…

A:

Q: Find f(x) if f(2) 5 and the tangent line at x has slope (x = 1)eX- 2x. %3D f(x) =

A:

Q: 14. Find the equation of the line tangent to the graph of f(x) = 2x3-x + 1 at x = -1. %3D

A:

Q: Find the slope of the tangent line to the graph of the functiony=f(x)=−6.5x^2 at point x=7

A:

Q: At what point on the graph of f ( x ) = 2 x 3 - 3 x 2 - 8 x is the tangent line equal to 4?

A:

Q: The slope of the tangent line to the graph of the function (16, 24) is - O 1.25 O 0.88 O -2.00 | O…

A: Given function -  f(X) = y = 7√x -4

Q: If the slope of the tangent line to the graph of f(x) at x is m(x)=3x^2-2x+1 and f(2)=4, then what…

A: The slope of the tangent line to the graph of f(x) at x is m(x)=3x2-2x+1 and f(2)=4.

Q: 14. Find a function whose tangent has slope 4x+1 for each value of x and whose graph passes through…

A:

Q: Here is the graph of the function h(x)on the interval (-5, 5), and part of a line tangent to h(x) at…

A:

Q: 3. Find the equation of the tangent line to the graph of f (x) =7-3x-x at x= 1 %3D

A:

Q: -2, find an If g(x) = xf(x), where f(3) = 4 and f'(3) equation of the tangent line to the graph of g…

A: Consider the given function gx=xfx

Q: The slope of the tangent line to the graph of the function y = 8VI - 4 at (16, 28) is O 1.50 O -1.75…

A: Given function is, y=8x-4

Q: Find an equation of the tangent line to the graph of y= g(x)at  x = 5 if g(5)  =-3  and g(5)  =4

A: Let us consider g(5)=-3 and g'(5)=4. The equation of a tangent line at the point x=5 on the graph…

Q: Find an equation of the tangent line to the graph of y=g(x) at x=2 if g(2) =-4 and g'(2)=3

A:

Q: Find an equation of the tangent line to the graph of f at the given point. (5-) X + 3 f(x) X -1 2

A: Find an equation of the tangent line to the graph of f at the given point. First differentiate the…

Q: 7) Find the tangent line to the graph of f (x) = 3 – 4e * at x =0.

A:

Q: Find the tangent line to the graph of f(x)=(x+1)/(x-1) at the point (2,3)

A: As we know that; The slope of the tangent line to the curve at a given point is equal to the first…

Q: 3. If f(x) = 5x - 8x, find the equation of the tangent line to the curve at the point where x= 2.

A:

Q: 3. Given that the graph of f passes through the point (2,5) and that the slope of the tangent line…

A:

Q: Find an equation of the tangent line to the graph of f(x) at the given point. f(x)= 2 / x^(3/4)  at…

A: Given function f(x)

Q: 6. Find the length of the curve given by the graph of the function f(x) = x/x, for x in [1,4].…

A:

Q: Suppose that f is a function defined as f(x) = 5x3 + 3x2 + x + 3. Find an equation for the tangent…

A: f(x)=5x3+3x2+x+3Derivative formuladdxxn=n xn-1

Q: The slope of the tangent line to the graph of the function y = 7 x – 3 at (9, 18) is. O -2.67 O 1.17…

A: We know that dy/dx gives slope of tangent at any point.

Q: If the slope of the tangent line to the graph of f(x) at x is m(x)=3x^2-x+1  and f(2)=4, then what…

A:

Q: Suppose that a one-to-one function f has tangent line y=5x+3 at the point . (1,8)Evaluate (f-1)'8

A:

Q: If the slope of the tangent line to the graph of f(x) at x is m(x)=3x^2-2x+1 and f(2)=4, then what…

A:

Q: Find the equation of Tangent line to the graph of f-1 at the indicated point p(2, 1) of the…

A:

Q: Find an equation of the tangent line to the graph of y = f(x) when x = 2 if f(2) = -6 and f'(2)= 5.…

A:

Q: 4. If f (2) = 3 and f'(2) = 5, find an equation of the tangent line at the point where x=2.

A: We have to find the equation of tangent.

Q: Find the points on the graph of f(x) = where the tangent line is horizontal. x2+2

A: Given query is to find the points where tangent is horizontal.

Q: Find the slope of the tangent line to the graph of f(x) at the point (1,2). The function is…

A:

Q: Find the length of the curve defined as: f (x) = 5x from x = 0 to x = 1

A:

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = 4 +9 In…

A:

Q: The slope of the tangent line to the graph of the function y = 8vT- 4 at (16, 28) is O 1.00 O -2.25…

A:

Q: Prove without graphing, that the graph of the function has at least two x-intercepts in the…

A:

Q: Find the function whose tangent line has the slope 8x² + 3 for each value of x, and whose graph…

A: To find the function:

Q: Find f (4) and f ,(4) if the tangent line to the graph of f at x = 4 has equation y = 3x − 14.

A:

Q: 22. If the tangent line to y = f(x) at (4, 3) passes through the point (0, 2), find f(4) and f'(4).…

A: #22 f(4) ? f'(4)?

Q: The slope of the tangent line to the graph of the function y = 7VI - 3 at (9, 18) is O -2.00 O 1.83…

A: Solution

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.