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Using the limit derivative of the derivative to find the slope of the tangent line to curve f(x)=4x^2 at x=3, what is f(3+h)?

Answer :

[tex]f(x)=4x^2[/tex][tex]f^{\prime}(x)=8x[/tex][tex]f^{\prime}(x=3)=8\cdot3=24[/tex]

the slope at x=3 is 24

for f(3+h)

[tex]f(3+h)=4(3+h)^2[/tex][tex]f(3+h)=4(9+2\cdot3\cdot h+h^2)[/tex][tex]f(3+h)=36+24h+h^2[/tex]

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