3.2 The Derivative as
a Function
a Function
The Definition of the Derivative
what is the limit as h approaches 0 of f(x+h)-f(x)/h
Power Rule
f(x)=An=>nAn-1=f'(x)
Find the derivative of
f(x)= 12x4+3
f'(x)=48x3
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)
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)
Use the Limit Definition of a Derivative to solve:
3x2-5x-3
The limit as h approaches 0 = 6x-5
The Constant Multiple Rule
f(x)=kf(x)=>f'(x)=k(d/dx)f(x)=kf'(x)
Find the derivative of
f(x)=(x2+4)(2x+7)
f'(x)=f'g+g'f=(2x)(2x+7)+(x2+4)(2)
The revenue function R(q)=-7q2+300q. What is the marginal revenue at 5?
MR(q)=R'(q)=R'(5)=$230
find f'(x)
f'(x)=10x4(sin(x))+2x5(cos(x))
Product Rule
f'(x)=f'(x)g(x)+g'(x)f(x)
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
Given a position function of s(t)=4t3-42t2+144t, at what time would the velocity equal 0?
at time t=3 and 4
An equation for the line tangent to f(x)=x2+cos(x) at x=0
y=1
Quotient Rule
f(x)=f(x)/g(x)
f'(x)=f'(x)g(x)-g'(x)f(x)/g(x)2