Derivative

App of first der

100

f’(x)>0

Increasing interval

200

f’(x)<0

Decreasing interval 

300

f’(x)=0

critical points

App of second der

100

f’’(x)>0

Concave up

200

f’’(x)<0

Concave down

300

f’’(x)=0

Inflation point

General Graph

100

Second step 

Even and odd

200

Fifth step

Continuty

300

Eights step

Second derivative test

Take Derivative

100

f(x)=2x³-21x²+72x+5

6x²-42x+72

200

f(x)=tan(5x-4)

5/cos²(5x-4)

300

f(x)= 3/(2x-1)⁴

-24/(2x-1)⁵