Homework

Problem 1 · easy

Find all critical points of f(x) = x^2 - 4x + 1.

Problem 2 · easy

Is x = 2 a local max or min for f(x) = x^2 - 4x + 1?

Problem 3 · easy

Find all critical points of f(x) = x^3 - 3x + 2.

Problem 4 · medium

Find the local max value of f(x) = x^3 - 3x + 2.

Problem 5 · medium

Where is f(x) = x^4 - 4x^3 increasing?

Problem 6 · easy

Find the inflection point of f(x) = x^3.

Problem 7 · medium

Find the inflection points of f(x) = x^4 - 6x^2.

Problem 8 · medium

Find the absolute max of f(x) = x^2 - 2x on [0, 3].

Problem 9 · medium

Find the absolute min of f(x) = x^2 - 6x + 5 on [0, 5].

Problem 10 · medium

Find critical points of f(x) = 3x^4 - 8x^3.

Problem 11 · easy

On what interval is f(x) = x^2 - 4 concave up?

Problem 12 · easy

On what interval is f(x) = -x^2 + 4 concave down?

Problem 13 · medium

Find the x-value where f(x) = x^3 - 6x has a local min.

Problem 14 · medium

State the MVT guarantee for f(x) = x^2 on [1, 3].

Problem 15 · medium

How many critical points does f(x) = x^5 - 5x^4 have?

Problem 16 · medium

Find the absolute max of f(x) = sin(x) on [0, pi].

Problem 17 · medium

Where does f(x) = x^3 - 12x have a local maximum?

Problem 18 · medium

Find all inflection points of f(x) = x^3 - 6x^2 + 9x.

Problem 19 · medium

Is x=0 a local max, local min, or neither for f(x) = x^3?

Problem 20 · easy

Find the global minimum of f(x) = x^2 + 1.

Problem 21 · easy

What does the MVT guarantee if f is constant on [a,b]?

Problem 22 · easy

Find the local min value of f(x) = x^3 - 3x at x = 1.

Problem 23 · challenge

Find all x where f(x) = x^4 - 2x^2 has inflection points.

Problem 24 · challenge

For f(x) = x^3 - 9x^2 + 24x on [0, 5], find the absolute max value.

Problem 25 · medium

Does Rolle's Theorem apply to f(x) = |x| on [-1, 1]? Yes or no.