Let be the function defined by .

MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let

f

be the function defined by

f(x)=e^{x^{2}}

. (a) Calculate

f'(x)

. (b) Write the equation of the line tangent to the graph of

f

x=0.5

in point–slope form and then simplify to slope–intercept form. (c) Use the tangent line found in part (b) to approximate the value of

f(0.51)

. Clearly show all work leading to your approximation.