If f(x) = 4x? + 5x + 3, find f' (-5), using the definition of derivative. f' (-5) is the limit as a → -5 of the expression 8x+5 ·The value of this limit is -35

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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why is 8x+5 wrong? what is the correct answer? ):

If \( f(x) = 4x^2 + 5x + 3 \), find \( f'(-5) \) using the definition of the derivative. \( f'(-5) \) is the limit as \( x \to -5 \) of the expression

\[ 8x + 5 \]

The value of this limit is

\[ -35 \]

Use this to find the equation of the tangent line to the parabola \( y = 4x^2 + 5x + 3 \) at the point \((-5, 78)\). The equation of this tangent line can be written in the form

\[ y = -35x - 97 \]
Transcribed Image Text:If \( f(x) = 4x^2 + 5x + 3 \), find \( f'(-5) \) using the definition of the derivative. \( f'(-5) \) is the limit as \( x \to -5 \) of the expression \[ 8x + 5 \] The value of this limit is \[ -35 \] Use this to find the equation of the tangent line to the parabola \( y = 4x^2 + 5x + 3 \) at the point \((-5, 78)\). The equation of this tangent line can be written in the form \[ y = -35x - 97 \]
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