5. Suppose that function f(x) satisfies f'(x) < 0, f (x) > 0 at interval [a, b], then the graph of y = f(x) ( ) over this interval. (A) increasing and concave upward (B) increasing and concave downward (C) decreasing and concave upward (D) decreasing and concave downward

Q: Let f(x) = (x³ +2x+4)* ƒ'(x) = = ƒ'(1) =

A: The function is f(x)=(x3+2x+4)4the aim is to find the derivative then the derivative of the function…

Q: For the function f(x) =-X find f"(X), f"(0), f’"(1), and f"(- 1). "(X) = O I7

A:

Q: Evaluate the function when x = 1, 3 and 3 3 1) f(x) = x + 2x - 3

A:

Q: Find y' if 3x2- (xy²) = 2y³ 2 3=

A: Given: 3x2-xy212=2y3   As we know that; The sum/difference rule: f±g'=f'±g' The Power law;…

Q: Determine the values of x for which f (x)=x",x >0 is increasing or decreasing.

A:

Q: Find f. f "(x) x2, x > 0, f(1) 0, f(9) 0 =

A: Given,

Q: Assume that the function f is a one-to-one function. (a) If f(5) = 2, find f-'(2). Your answer is…

A: Given that to he function f is one-to-one function.

Q: Use the graph of f(x) to find the interval where f''(x) > 0. Ⓡ 3- 2- 1- ms -5 -4 -3 -2 -1 1 3 4 5 A.…

A: Here we have given the curve of f(x)  Now to determine all x value where  f"(x) &gt; 0

Q: Use the graph of f(x) to find the interval where f''(x) > 0. -5 -4 -3 -2 -1 3- 2- 2 -3₂ 4 T 5 A.…

A:

Q: 5. Sketch the graph of one function f(x) that has all of the following properties: a.) f(-2) 0 b.)…

A: As per our guidelines we are supposed to answer  only one question. Here question 5) answer.

Q: 5. Sketch the graph of a function f(x) satisfying the following properties: f(2) = 3 f(-3) = 0 f'(2)…

A:

Q: Identify the equation that defines y as a function of x (a) x+(y-1)² = 3 (b) x2-y 3xy (c) 3x+5y = 1…

A: (a) x + (y-1)^2 =3       this equation gives two value x (b) x2 - y2=3xy    it also give two values…

Q: In Exercises 13–-16, refer to Figure 14.

A: To Determine: show that f'(3) does not exist . Given: we have a graph of f. Explanation: from the…

Q: Compute

A:

Q: Sketch the graph of f(x) = xª – 2.x² + 7 using graphing strategy (analyze f, f' and f").

A: Consider the graph of f(x).

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.