Calc I Quiz #2

3.2 The Derivative as a Function

100

The Definition of the Derivative 

what is the limit as h approaches 0 of f(x+h)-f(x)/h 

200

Use the Limit Definition of a Derivative to solve: 

3x²-5x-3

The limit as h approaches 0 = 6x-5

Differentiation Rules (Formulas)

100

Power Rule 

f(x)=Aⁿ=>nA^n-1=f'(x) 

200

The Constant Multiple Rule 

f(x)=kf(x)=>f'(x)=k(d/dx)f(x)=kf'(x) 

300

Product Rule 

f(x)=f(x)*g(x) 

f'(x)=f'(x)g(x)+g'(x)f(x) 

400

Quotient Rule 

f(x)=f(x)/g(x)

f'(x)=f'(x)g(x)-g'(x)f(x)/g(x)²

3.3 Differentiation Rules (Practice Problems)

100

Find the derivative of 

f(x)= 12x⁴+3

f'(x)=48x³

200

Find the derivative of

f(x)=(x²+4)(2x+7)

f'(x)=f'g+g'f=(2x)(2x+7)+(x²+4)(2)

300

Find the derivative of 

f(x)=(3x⁴-12x+5)/(3x)

f'(x)=f'g-g'f/g²=

(12x³-12)(3x)-(3x⁴-12x+5)(3)/(3x)²

3.4 The Derivative as a Rate of Change

100

The difference between marginal cost, and actual cost.

Marginal cost is the derivative of a cost function evaluated at a certain point C'(x), where as actual cost is a certain point tested in the cost function C(x) 

200

The revenue function R(q)=-7q²+300q. What is the marginal revenue at 5? 

MR(q)=R'(q)=R'(5)=$230 

300

Given a position function of s(t)=4t³-42t²+144t, at what time would the velocity equal 0? 

at time t=3 and 4

3.5 The Derivatives of Trig Functions

100

The "full cycle wheel" of the derivative of sin(x) 

f(x)=sin(x)

f'(x)=cos(x)

f''(x)=-sin(x)

f'''(x)=-cos(x)

f''''(x)=sin(x)

200

f(x)=2x⁵tan(x)/sec(x)

find f'(x)

f'(x)=10x⁴(sin(x))+2x⁵(cos(x))

300

An equation for the line tangent to f(x)=x²+cos(x) at x=0

 y=1