Given the function g(x) 4x³ + 6x? – 240x, find the first derivative, g'(x). g'(x) Preview Notice that g'(x) = 0 when x 5, that is, g'( – 5) = 0. Now, we want to know whether there is a local minimum or local maximum at x = will use the second derivative test. Find the second derivative, g''(x). – 5, so we g''(x) = Preview Evaluate g''( – 5). g''( – 5) = Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at x = At x = 5? 5 the graph of g(x) is Select an answer Based on the concavity of g(x) at x = local maximum at x = At x = – 5, does this mean that there is a local minimum or 5? – 5 there is a local Select an answer

Q: Find the derivative a. f(x)= 6/(3x2-pi)4 b. f(x)=((3x2-pi x)4

A: (a) given,

Q: Given f''(x) = 8x- 2 and f'(- 2) = – 2 and f(- 2) = 3. Find f'(x) = and find f(3)

A: Solution:

Q: Differentiate the function.

A:

Q: If f(x) = 3x² − 5x+7, find f'(-5). | Use this to find the equation of the tangent line to the…

A:

Q: Use technology to find f'(2), f'(15), f'(-3) for the given function when the derivative exists. f(x)…

A: Step 1:   Step 2: Step 3: Step 4:

Q: The graph of the function f(x) = x³ – 3x has one local maximum and one local minimum point. Find…

A: Given function is: fx=x3-3x

Q: Find the absolute maximum and minimum, if either exists, for f(x) = x - 8x + 9. Find the first…

A:

Q: Find the original function f(x) from given equation f'''(x)

A: We can solve this as follows:

Q: Find the higher-order derivative. f"(x) = 12x³ - 38x² f(x) = 72 X

A:

Q: The product of two numbers x and x + 170 can be simplified to be x + х.

A:

Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: f'(x)=-2x8-x2;(2,8)

Q: What rule do you use to calculate the derivative of f(x) = exx2 and f(x)=(x2-3x+1)/(x+5) ?

A: Use the product rule and quotient rule of derivative: