14. Are the functions continuous on the given interval? 7 (a) f(x) = 3 x € [1,7] and (b) g(x)=2x²-₁, x € [−5, 4]. 2 x- 5 x+1'

Q: f(x) = (x² + In x)(x³ + 4x + 5) f(x) = (x2+5x) In x (Vx-6x)e* %3D

A: We have to find the derivative for each of the functions. 1. fx=x2+lnxx3+4x+52. f(x)=x2+5xlnxx-6xex

Q: Given this graph of f'(x), prove which of the following symbols is appropriate to put in the blank.…

A: Here, from the given graph: f'(x)<0 on (-∞,-2)∪(0,6) So, f is decreasing on -∞,-2)∪(0,6

Q: 4. Let f be the function given by f(x) = 4-x. g is a function with derivative given by g'(x) =…

A: Given f( x ) = 4 - x

Q: For the function y = h(x) whose graph is shown, find the values of x such that the derivative is…

A: For the given function: y=hx The graph shown is:

Q: f(x) = 3x² + 5x -6 find f'(x) 6x-6 O 3x-5 O 6x +5 none of these ansswers

A: The given function fx=3x2+5x-6. We have to find f'x.

Q: 28. For each function, sketch the graph of y = f(x) and find an expression for f'(x). Indicate any…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 3. (a) Given the function f(x) = 2x³ + 3x² − 12x + 1. Using the derivative formulas, find f'(x). (b)…

A: Given,

Q: Let f be a function defined on the closed interval -4sxs4. The graph of f', the derivative of f, is…

A: Let's find.

Q: Determine the values of the constants a and b which make the function f(x) below continuous at x =…

A: A function f(x) is continous at x = a when:

Q: x-2 For the function 10x) = ind f(X), the third denvative of t and i ), the fourth derivative ofT…

A: Please refer the attached image for complete solution.

Q: If f(x) = 5x4 - 2e, find: ƒ'(x) = f'(3)= f''(x) = f''(3) =

A:

Q: 10. Find the derivative function for f(x) = √ x + √x + √x + √x + ... √ + +....

A:

Q: 40. Define the function f by f(x) = tan (e*). The graph of f intersects the x-axis once in the…

A: f(x) = tan(ex ) f'(x) = sec2(ex) . ddxex f'(x) = sec2(ex). ex

Q: A company has found that the cost, in dollars per pound, of the coffee it roasts is related to C'(x)…

A: A company has found that the cost, in dollars per pound, of the coffee it roasts is related to for…

Q: Q: Use the Second Derivative Test to classify the local extremes of the function f(x,y) =…

A:

Q: 5. Use the graph of f(x) = x' - 2x and g(x) =x to answer the questions. (a) For what values of x is…

A: Given that, f(x)=x3-2x, g(x)=x For f(x)=g(x), we have, x3-2x=x⇒x3-3x=0⇒x(x2-3)=0 This gives x=0, ±3…

Q: If the point A (4,3) and B(x,5) are on the circle with centre 0 (2,3). Find the Value of x

A:

Q: Differentiate the function. f(x)= -1 x+5 f'(x)3D

A:

Q: The graphs of the function F (left, in blue) and G (right, in red) are below. Let P(x) = F(x)G(x)…

A: Graph of the functions Fx and Gx are given and Px=FxGx and Qx=FxGx. We have to find the values of…

Q: 4. Using the definition of the derivative, find f'(x) for each function f(x). State the domain of…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Show solution. 1. Below is the graph of f(x) = |x]. Using the right side of the function with the…

A: The given function,   y=x