Assessment: Applications of Derivatives

Find f'(x) for f(x) = 5x² + cos(x).

Find the critical point of f(x) = x² − 6x + 5.

f(x) = x² − 6x + 5 has a critical point at x=3. Is f increasing or decreasing on (3, ∞)?

Is f(x) = x³ − 3x concave up or concave down at x=2?

Find the absolute minimum of f(x) = x³ − 3x on [0, 2].

For f(x) = x³ − 3x, use the Second Derivative Test to classify the critical point at x = −1.

A technician needs a quick estimate of √9.1 without a calculator, using linear approximation at a=9 (f(9)=3, f'(9)=1/6). What is the estimate?

A ball thrown into the air reaches its peak height at the exact instant its velocity (the derivative of height) equals zero. What is this instant called in calculus?

Find the absolute maximum of f(x) = x³ − 3x on [−3, 3].

Using f(x)=∛x and a=8 (f(8)=2, f'(8)=1/12), estimate ∛8.3.