using the definition of derivative f´(x)=limh-->0 (x+h)-f(x) /h enter the expresion needed find the derivative at x=3 f¨(x)=lim h->0 after evaluating this limits, we see that f¨(x)=   f¨(x)=lim h-->0   finally the equation of the tangent line to f(x) in point lope form, where x=3 is

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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let f(x)=4x2 +12x-2

using the definition of derivative f´(x)=limh-->0 (x+h)-f(x) /h

enter the expresion needed find the derivative at x=3

f¨(x)=lim h->0

after evaluating this limits, we see that f¨(x)=

 

f¨(x)=lim h-->0

 

finally the equation of the tangent line to f(x) in point lope form, where x=3 is  -----------

 

f¨(x)= limh-->0 f(x+h)-f(x) /h

 

equation of tangent line to f(x) at x=x0  is y=f(x0 )=f¨(x0 )(x-x0 )

 

 

 

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