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Section 1

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Derivative of f(x) (notation)

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Calculus Math

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Mar 1, 2020

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Section 1

(14 cards)

Derivative of f(x) (notation)

Front

F'(x) or d/dx f(x)

Back

F(x) is continuous at x=a if...

Front

1) f(a) exists 2) lim x~a f(a) exist 3) lim x~a. f(x)=f(0)

Back

Alternate limit definition of the derivative of f(x) at x=a

Front

lim (as) x~a f(x)-f(a)/x-a

Back

point slope form

Front

y-y₁=m(x-x₁)

Back

IVT (Intermediate Value Theorem)

Front

SHOW: 1) F is continuous on [a,b] 2) K is any y-value between f(a) and f(b) CONCLUDE: The IVT guarantees that there's at least one x-value c between a and b such that f(c)=k

Back

Limit definition of the derivative of f(x)

Front

lim (as) h~0 f(x+h)-f(x)/h

Back

The Power Rule: d/dx x^n

Front

nx^n-1

Back

Derivative (definition)

Front

Slope at a point

Back

d/dx C where c is a constant

Front

0

Back

d/dx c f(x)

Front

Cf'(x)

Back

lim (as) x~a f(x) exists if...

Front

lim (as) x~a f(x)= lim (as) x~a^- f(x)

Back

Equation of line tangent to f(x) at x=a

Front

Y-f(a)=f'(a)(x-a) or Y=f'(a)(x-a)+f(a)

Back

Sum Rule: d/dx f(x) + g(x)

Front

F'(x) + g'(x)

Back

A function is not differentiable at an x-value if there is a:

Front

Hole, jump, V.A, sharp turn, or vertical tangent line

Back