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# Math 153 Exam #3 Study Guide MATH 153

WVU

GPA 3.5

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## Popular in Calculus 1A with Precalculus

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This 2 page Study Guide was uploaded by Sophia Valla on Sunday October 16, 2016. The Study Guide belongs to MATH 153 at West Virginia University taught by Andy Blankenship in Fall 2016. Since its upload, it has received 11 views. For similar materials see Calculus 1A with Precalculus in Math at West Virginia University.

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Date Created: 10/16/16

Math 153 Exam #3 Study Guide Derivative lim f (x+h)− f (x) h→0 d❑ f f (x)= h → d ❑ x Instant Rate of Change x→a f (x)− f (a) x−a Equation of a Tangent Line ● Tangent line passes through a graph f(x) at one point ● Secant line passes through two points 1. Tangent line is always linear (y=mx+b) 2. Slope of f(x) at the point where the tangent lines matches is the slope (m) 3. The curve f(x) and tangent line shares 1 point (a,f(a)) ● Two points are used to find the slope ● A point and a derivative are used to find the equation of a tangent line Slopes of Graphs 1. If f(x) is increasing a. Slope = positive b. 1 above xaxis f ❑ 2. If f(x) is decreasing a. Slope = negative b. f ❑1 below xaxis 3. If f(x) is constant a. Slope = 0 b. f ❑1 is on the xaxis 1 f ❑ does not exist Discontinuous Sharp points (cusps) Where slope is undefined (vertical tangent line) Derivative of Polynomials Is c is any real number (constant) then… d dx (c) =0 Power Function d f ❑ (x)= (x❑ )=nx❑ n−1 , n is any real number is power function dx d d d ● [f(a)+g(a)] = (f(x))+ (g(x)) dx dx dx d d d ● dx [f(x)g(x)] = dx (f(x)) dx (g(x)) ● d (cf(x)) = c d (f(x)) dx dx When to not use power rule 1. f (x)= 1 x❑ n n m n m f (x)= x❑ +x❑ → x❑ + x❑ 2. x❑ p x❑ p x❑ p n m 3. f (x)=x❑ ∗x❑ ● f ❑ (x) = a❑ ∗ln(a) x 1 x x x f (x)=e❑ → f ❑ (x)=e❑ ∗ln(e❑ )=e❑ Product Rule 1 1 1 y❑ = f (x)∗g❑ (x)+ f ❑ (x)∗g(x) ● No use when denominator has more than 1 term Quotient Rule 1 1 y❑ = g(x) f ❑ (x)− f (x)g❑ (x) [g(x)]❑ 2 ● “Low, dhigh” minus “high, dlow”, over square of what's below

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