Question

A curve has equation y=x√x.find the equation of the tangent to the curve at the point(1, 5)

Answer 1

Answer:

y - 5 = $\frac{3}{2}$(x - 1)

Step-by-step explanation:

Note that $\frac{dy}{dx}$ = $m_{tangent}$

Differentiate using the power rule

$\frac{d}{dx}$(a$x^{n}$) = na$x^{n-1}$

Given

y = x$\sqrt{x}$ = x. $x^{\frac{1}{2} }$ = $x^{\frac{3}{2} }$, then

$\frac{dy}{dx}$ = $\frac{3}{2}$$x^{\frac{1}{2} }$

When x = 1

$\frac{dy}{dx}$ = $\frac{3}{2}$ . 1 = $\frac{3}{2}$

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = $\frac{3}{2}$ and (a, b) = (1, 5), thus

y - 5 = $\frac{3}{2}$(x - 1) ← equation of tangent