Let f(x) and g(x) be differentiable functions such that • f(3) = 1, f(0) = f'(3) = 2. • g(1) = 0, gʻ(1) = 2. (a) Set h(x) : = (f^(3x) + 5g(2)". + 5g(x))". %3D Explain why is ha differentiable function and find h'(1). (b) Set s(æ) = tan a² + f(x)g(2x + 1) . Find s'(0).

Q: f'(c)=f(b)-f(a)/b-a .Use the Mean Value Theorem to find the number c for the function f(x)=x3-3x+2…

A:

Q: Express the function in the form   f ° g  ° h

A: We will use the most inner function=h(x), then next one=g(x), and the outer one=f(x)

Q: f(x) = 4x^3-(x+9)^1/2 What is the interval or intervals on which the function is differentiable on…

A: Refer  to the question the provided function is f(x) = 4x^3-(x+9)^1/2.

Q: Find f'(x) if f(x) = 1 (x+csda4+10))³

A: *concept:- cscx = 1/sinx. d/dx (sinx) = cosx. d/dx (x^{n}) = nx^{(n-1)}

Q: Let f(x) = 2x ^ 3 – 7x + 3x ^ 7 – 2. Find the 4th order derivative evaluated at x=2. A

A:

Q: If the given three vectors are coplanar, then find the value of x. A = i-2j + 3k, B = xj + 3k, C =…

A: A, B, C are coplanar.So

Q: Explain and sketch how a function can have f ''(a) = 0 at (a, f(a)) and not be an inflection point.

A: It is given that f''(a)=0 at (a, f(a)). The objective is to explain and sketch how a function can…

Q: Given the function f(x) = x-7, x > 0, (a) Find f'(x).

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: