INTRO TO CALC - REVIEWER

Front

What is the slope of the secant line for the function f(x) = 3 - 2x^2?

Back

Front

How do you find the derivative of the function f(x) = (x + 4)(2x - 5)?

Back

Use the product rule: f'(x) = (x + 4)'(2x - 5) + (x + 4)(2x - 5)'. The derivative is f'(x) = 4x + 3.

Front

What is the derivative of f(x) = x^7 - 2x^4 + 5x^2 - 3x + 9?

Back

The derivative is f'(x) = 7x^6 - 8x^3 + 10x - 3.

Front

What is the Power Rule in calculus?

Back

The Power Rule states that if f(x) = x^n, then f'(x) = nx^{n-1}.

Front

Find the derivative of f(x) = 3x^7 - 4x^5 - \frac{1}{3}x^3 + x^2 - 3x + 7.

Back

Using the Power Rule, the derivative is f'(x) = 21x^6 - 20x^4 - x^2 + 2x - 3.

Front

How do you find the equation of a line given two points (8, 8) and (2, 4)?

Back

First, find the slope m = (y2 - y1)/(x2 - x1). Then use the point-slope form to find the equation.

Front

What is the formula for the slope of a line?

Back

The slope m is calculated as m = (y2 - y1)/(x2 - x1).

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is 0.

Front

What is the product rule for derivatives?

Back

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

Front

What is the quotient rule for derivatives?

Back

If u(x) and v(x) are functions, then (u/v)' = (u'v - uv')/v^2.