Suppose that f'(x) = (x − 1)³x² x + 3 Determine the interval(s) on which y = f(x) is decreasing.

Q: If f(x) = (2x2 – 5)(2x + 2), find f '(x).

A:

Q: If f(x) = 5x² – 2e*, find f '(x).

A: Given that  f(x) = 5x2 - 2ex  We need to find f'(x) and f"(x) . Now , f(x) = 5x2 - 2ex  So,   f'(x)…

Q: If f(x) - 5', show that f(x + h) – f(x) 5" h h

A: given that f(x)=5^x

Q: 2. Determine f'(1) for the function f(x) = (8x – 6Vx5 + 3) (x² – 9x² +) -

A: A detailed solution is given below

Q: Find f"(x). f(x) = (x? +7) °

A:

Q: 3 find f'(x). x2 7 If f(x) = 7+ -+

A:

Q: rsin(r2) Let g(x) 1 and f(x) g(t) dt. Find f' (2). xª + 1

A: From the given information we can apply the fundamental theorem of calculus.

Q: Find f. f"(x)  =20x3 -12x2 +6x

A: Consider the provided function, f''x=20x3-12x2+6x Find  fx. Integrate both the sides with respect to…

Q: Suppose f(x)=x^4+3x+1 on the interval [−4,−1]. Find x when f′(x)=0.

A: Given function is Differentiating with respect to x , we get

Q: Find f. f"(x)  =x6 - 4x4 +x +1

A: ∫xndx = xn+1n+1+C

Q: function of xx if

A:

Q: Find the general form of f if f'(x)= -7f(x).

A:

Q: Differentiate the function G(x) = 7x7 +5x-⁹.

A: Introduction: Apart from integration, divergence is among the two key ideas of calculus. A technique…

Q: find f'(t) for f(x)=x/8x-8

A: We will need the quotient formula to find f'(x) Assume u and v, then find u' and v'

Q: Use your answer from the last problem to find f'(-3) for f (x) = 3x² – 4x + 2.

A:

Q: Use the graph of f(x) to find the interval where f"(x) > 0. O A. (0,00) O B. (0,3) OC. (-3,00) O D.…

A: We need to find interval where f''(x) will be positive.

Q: Calculate f"'(-1) for f(x) = 3x 5 - 2x 2 + 1x- 2 .

A: Consider the given function, fx=3x5-2x2+1x-2 here the objective is to find the value of the third…

Q: If f(x) = (4x – 2)² - (3x² + 6)", find f'(4).

A:

Q: Define the function f(x) , whose derivative is f′(x)=5x2+6x+4  and whose graph passes through the…

A: Derivative