The slope of the curve at the point (4, 48) is 24.
PROBLEM 2. Find the derivative of f(x) = 3x^2.
Answer: f(x + h) = 3(x + h)^2 = 3x^2 + 6xh + 3h^2 . Use the definition of the derivative.
Simplify.
The derivative is 6x.
PROBLEM 3. Find the derivative of f(x) = x^3.
Answer: f(x + h) = (x + h)^3 = x^3 + 3x^2 h + 3xh^2 + h^3 . First, use the definition of the derivative.
And simplify.
= (3x^2 + 3xh + h^2 ) = 3x^2The derivative is 3x^2.
This next one will test your algebraic skills. Don’t say we didn’t warn you!
PROBLEM 4. Find the derivative of f(x) = .
Answer: f(x + h) = .
Use the definition of the derivative.