Homework

Problem 1 · easy

Use the definition to find f'(x) for f(x) = 3x.

Problem 2 · easy

Use the definition to find f'(x) for f(x) = x^2 + 1.

Problem 3 · easy

Find f'(x) for f(x) = x^4.

Problem 4 · easy

Find f'(x) for f(x) = x^7.

Problem 5 · easy

Find the derivative of f(x) = 12.

Problem 6 · easy

Differentiate f(x) = 5x^3.

Problem 7 · easy

Differentiate f(x) = 4x^2 - 3x + 7.

Problem 8 · easy

Differentiate f(x) = x^3 - 5x^2 + 2x - 1.

Problem 9 · medium

Find the derivative of f(x) = 6x^5 - x^3.

Problem 10 · medium

Find f'(x) for f(x) = 2x^4 - 7x^3 + 3x - 4.

Problem 11 · easy

Find the slope of f(x) = x^2 at x = 5.

Problem 12 · easy

Find the slope of f(x) = x^3 at x = 2.

Problem 13 · medium

Find the equation of the tangent line to f(x) = x^2 at x = 1. Give the y-intercept.

Problem 14 · medium

Find f'(x) for f(x) = x^(1/2).

Problem 15 · medium

Differentiate f(x) = x^(-2).

Problem 16 · medium

If s(t) = t^2 + 4t, find the velocity at t = 3.

Problem 17 · medium

If s(t) = 3t^3 - 2t, find v(t).

Problem 18 · challenge

Find f'(x) for f(x) = 9x^(2/3).

Problem 19 · challenge

Find where the tangent line to f(x) = x^2 - 4x is horizontal.

Problem 20 · challenge

Find all x where f(x) = x^3 - 3x^2 has a horizontal tangent.

Problem 21 · medium

Differentiate f(x) = 7x^4 - 2x^2 + x.

Problem 22 · easy

If f(x) = x^2 and g(x) = 3x, find (f + g)'(x).

Problem 23 · easy

Find the derivative of f(x) = (1/3)x^3.

Problem 24 · easy

Find f'(2) for f(x) = 5x^2 - 3x.

Problem 25 · medium

Find f'(-1) for f(x) = x^3 + x^2.