Calculus – Find the Tangent line Equation at Point (-1,1)

By | October 29, 2016

Find the Tangent line Equation at Point (-1,1)

In this tutorial students learn how to find the equation of the tangent line given the function and the point of tangency. The students then verify the solution using the GRAPH, WINDOW, CALC, TANGENT and TRACE features of the TI-84C.

Explicit Function

$y=f(x)=\sqrt[3]{x^2}$

Point of Tangency

$(-1,1)$

Derivative

$y'=f'(x)=\frac {2} {3\sqrt[3]{x}}$

Slope

Substitute in the x value from the point of tangency.
$y'=f'(-1)=\frac {2} {3\sqrt[3]{(-1)}}=-\frac {2}{3}$

Tangent Line

$y=-\frac{2}{3}x+\frac{1}{3}$