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: 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: (c) Let u(x, t) satisfy the hyperbolic system 4u, - u = 4 cos(t), xe R, t > 0. i. Find a general…

A:

Q: et f and g denote differentiable functions. If f'(x) = g (x), then f(x) = g(x).

A:

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: The domain of the function f(x)= tanh(18 - ) is (289, A), Then The value of k= %3D The value of A =

A:

Q: determine f given f' and a point which statify f. f'(X)= 4x3-3x2+2x (3,80)

A: To determine f given f' and a point which statify f.   f'(X)= 4x3-3x2+2x (3,80)

Q: Determine the interval(s) for which f(x)=96x^2-x^4  is concave up.

A: Given function is: fx=96x2-x4 Differentiating we get, f'x=ddx96x2-x4f'x=962x-4x3f'x=192x-4x3

Q: a)_f(x)= x+3 x²+3x x²-3x b) f(x)== c) f(x) = |x³ − 1| -

A: Differentiability

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: At which interval of x is the function of P(x)=(sqrt(1-x^2)) discontinous?

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

A:

Q: This function f(z)=(x^3-3xy^2)+i(3x^2 y-y^3) is differentiable O True False

A: Given :f(z)=x3-3xy2+i3x2y-y3

Q: The expression dy/dx = x(cube root^3 y) gives the slope at any point on the graph of the function…

A: Consider the differential equation dydx=fx,y with the initial condition yx0=y0. Substitute the…

Q: Find the derivative of the given function. f(x) = (2x² + 2)³(x² - 1)² f'(x) 80x⁹ +64x7 - 96x5 − 64x³…

A: To find the points at which the tangent line is horizontal, we have to find where the slope of the…

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: