Tutorial Exercise
Find an equation of the tangent line to the curve at the given point. Illustrate by graphing the curve and the tangent line on the same screen.
y = 8x - 7\sqrt{x}, (1, 1)
Step 1
We can find the equation of a line by using the Point-Slope formula $y - y_0 = m(x - x_0)$. This means that we need to find the slope $m$ of the line and a point $(x_0, y_0)$ on the line.
We begin by finding the slope. The line tangent to $y$ at $(x_0, y_0)$ will have the slope $m = f'(x_0)$. We have $y = 8x - 7\sqrt{x}$. Since $\sqrt{x} = x^{1/2}$, then