Math Test 3 Flashcards
A tangent line is
Only touches a point of a curve, locally speaking
A secant is
A line connecting two points of a curve
How to find the slope of a secant line
(Y2-y1/x2-x1) like all slopes
How to find slope of tangent line
Find the derivative of the secant’s slope or use the formula (f(x)-f(a))/(x-a)
See page 52 for details
Derivitative at a point
F’(a)=f(x) -f(a)/x - a
Derivitave at a whole funciton
Limit as h approaches zero is
F’(x)=f(x+h) -f(x)/h
*always plug in 0 for h
True or false: d/dx =f’(x)
True
Power rule of derivativex
F’(x^n) = nx^(n-1)
Note:sqrt(x) = x^(1/2) and ^d sqrt(x^n) =x^(n/d)
See pg54
Only applicable when:
- base is just x (not 5x+5 par example)
- the exponent is a contstant (not ^5x)
- the base is x and the expnent is a constant (not 4^x)
Steps for finding derivative in calculator
F3, open parenthesis, then (whatever the function is), comma, x, close parenthesis
What is the derivative of a constant?
Zero. Always Example: f'(x)=7 7-7/h 7-7/0 0/0
Derivative formula 1
D/dx(k*f(x))=
K*d/dx((f(x))
Derivatvie rule:
D/dx(f(x)+g(x))=
D/dx(f(x)+d/dx(g(x))
Derivtive rule
D/dx(f(x)-g(x))
=d/dx(f(x)-d/dx(g(x))
Limit rule
Lim(k*f(x))=
K*lim(f(x))
Lim(f(x)+g(x))
=lim(f(x)+lim(g(x))
Limit rule
D/dx(f(x)-g(x)=
D/dx(f(x)-d/dx(g(x)
The product rule for limits
Lim(f(x)g(x)) =lim(f(x))lim(g(x))
True or false: the derivative of a product is the product of its derivatives
False. The product rule for limits is not the same as the product rule for derivatives
The product rule of derivatives
D/dx(f(x)g(x))=d/dx(f(x))g(x)+f(x)*d/dx(g(x))
The quotient rule (of derivatives)
Derivative of (f(x)/g(x))=((derivative of f(x))*g(x) - f(x) *(derivate of g(x)))/ (g(x))^2
Or
(F/g)’=(f’g-fg’)/g^2
When do you use chain rule?
Since you cant use the power rule to differentiate lets say (2x+4)^3, you have to use the chain rule instead.
Chain rule
Derivative of ((g(x)^n))=n*g(x)^(n-1) * g’(x)
Bsically power rule times derivative
