Honors Calculus Unit 4 Review

Front

What is the second derivative of the function y = 3x^2 + 5x + cos(x)?

Back

f''(x) = 6 - cos(x)

Front

Find the second derivative of f(x) = x^2 + e^x - cos(x).

Back

f''(x) = 2 + e^x + cos(x)

Front

If g(x) = x^5 + 3x and h is the inverse function of g, what is h'(4) given g(1) = 4?

Back

h'(4) = 1/8

Front

What is the second derivative of the function f(x) = 2x - 5x^6?

Back

f''(x) = -150x^4

Front

Find the derivative of g(x) = 4csc(x) - 6cot(x).

Back

g'(x) = -4csc(x)cot(x) + 6csc^2(x)

Front

What is the definition of a derivative?

Back

The derivative of a function measures the rate at which the function's value changes at a given point.

Front

What is the power rule for differentiation?

Back

If f(x) = x^n, then f'(x) = nx^(n-1).

Front

What is the product rule for differentiation?

Back

If u(x) and v(x) are functions, then (uv)' = u'v + uv'.

Front

What is the chain rule for differentiation?

Back

If y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).

Front

What is the definition of an inverse function?

Back

An inverse function reverses the operation of the original function, such that if f(g(x)) = x, then g is the inverse of f.