MCV4U Review

Zeros

100

f(x)=2x²+3x+1

x = -0.5, x = -1

200

g(x)=(x+1)e^2x

x = -1

300

F(x)= (x³-4x) / (x²-1)

x = 0, x = -2, x = +2

400

t(x) = x*sqrt(x-1)

x = 1 (Undefined on x<1)

500

h(x) = sin(x) + cos(x)

x = 3pi/4, x = 7pi/4

Turning Points

100

f(x)= (x³)/3+2x²+3x-6

f'(x)=x²-4x+3

(-3,-6) and (-1,-7.33)

200

g(x)=(x+1)e^2x

g'(x)=e^2x(3+2x)

(-1.5,-0.025)

300

h(x)=cos²x      on [0, 2pi]

h'(x)=-2cosxsinx

(0, 1), (pi/2, 0), (pi, 1), (3pi/2, 0), (2pi, 1)

400

f(x)=x³ + x² - x + 2

(-1,3), (1/3, 1.82)

500

f(x)= (x²+4)/(x²-4)

(0,-1)

In(ner re)flection

100

f(x)=e^x

There are no inflection points

200

f(x) = x / (x+1)²

f(x) = 2(x-2) / (x+1)⁴

(2, 2/9)

300

f(x) = 2sin(2x)     on [0, pi]

f'(x) = 4cos(2x)

f"(x) = -8sin(2x)

(0,0), (pi/2,0), (pi,0)

400

f(x) = x³ -3x² +7

(1,5)

500

f(x) = xe^x

f'(x) = e^x(1+x)

(-2, -0.27)

Critical Numbers

100

f(x) = (x+1) / (x-1)

V.A. and Critical Number @ x = 1

200

g'(x) = (2x+1)² / (5x-1)(x+2)

Critical number @ x = 1/5, -2

300

f(x) = (x²+2x-1) / (x+1)²

Find critical numbers for f'(x)

Critical number @ x = -1 ^{Triple root}

400

f(x) = sqrt(x+1)

Find critical numbers for f'(x)

Critical number @ x = -1

500

f(x)= (x²+4) / (x²-4)

Find the critical numbers for f"(x)

Critical numbers @ x = 2^{Triple root}, -2^{Triple root}