AP Calculus Review Day 1 2024-2025

$$\frac{f'(x)g(x)-g'(x)f(x)}{\left(g\left(x\right)\right)^2}$$

$$\frac{f\left(b\right)-f\left(a\right)}{b-a}$$

$$y-y_1=m\left(x-x_1\right)$$

f'(x)g(x) +g'(x)f(x)

$$e^x$$

(- $$\infty$$ , -3)

(5, $$\infty$$ )

(-2,2)

(4, $$\infty$$ )

concave down

decreasing

critical points

increasing

concave up

the f'(x) changes from postive to negative, the f(x) has a relative maximum

the f'(x) changes from negative to positive, the f(x) has a relative minimum

the f''(x) changes from postive to negative, the f(x) is concave up

the f''(x) changes from negative to positive, the f(x) is concave down

$$0$$

$$\frac{1}{2}$$

$$1$$

$$\frac{\sqrt{2}}{2}$$

$$\frac{\sqrt{3}}{2}$$

top functions are the f(x), the bottoms ones are the f'(x)

top functions are the f(x), the bottoms ones are the f''(x)

top functions are the f'(x), the bottoms ones are the f(x)

top functions are the f''(x), the bottoms ones are the f(x)

first derivative test

2nd derivative test

increasing and decreasing

concave up and concave down

the definition of the derivative

the definition of limits

the equation of the tangent line

average rate of change