Find the first derivative f' and the original function f. f"(x) = x³ - 12x, ƒ'(1) = 0, ƒ(1) = 10

Q: Find f.   f ''(x) = (5/6)x5/6

A: Consider f''x = 56x56

Q: Find the first and second derivative of the function. Check to see that your answers are reasonable…

A: This question is related to differentiation, we will use basic rules of differentiation to solve it.

Q: .......

A: To find one x value where f'(x)=0. That is the tangent at x is parallel to x-axis.

Q: 27. y = x²(1 - In x²)

A: To find the derivative of the following function.

Q: Find the derivative of the function and then evaluate at the given point. y = 2x - 3x; (- 1,5) f'(x)…

A: f'(-1) = - 7  The detailed solution is as follows below:

Q: Find the derivative. F'(x) if F(x) = (ex³ + 8)ª

A:

Q: One x value where f '(x) is positive.

A:

Q: Find the derivative of the function h(w) = -7w¯4 +6/w. %3D h'(w) :

A: The function is  h(w) =-7w-4+6w. We know that derivative of wn, i.e., dwndw = nwn-1.

Q: Find the derivative of the function and then evaluate at the given point. y= 4x2 - 5x; (– 1,9) f'(x)…

A: The given function is y=4x2-5xThe point is (-1, 9)

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

A:

Q: Find the function of the derivative f'(x)= -12x+5 and with the graph passing through (-2,5)

A: Given, f'(x)= -12x+5

Q: One x value where f '(x) is negative.

A: fI(x) is the slope of the graph at any point . So, we will try to find the slope value at all points…