Find the equation of the tangent line to the curve y=x√x at the point (4,8).

Question

Find the equation of the tangent line to the curve y=x√x  at the point (4,8).

ash2326 · Answer

@jalotaibi Can you find the derivative of $y=x\sqrt x$    ?

anonymous · Answer

√x +(x^1/2)/2 ?

ash2326 · Answer

Yeah you're correct,
We know that the slope of tangent drawn at a point say (a, b)  is the$\large \frac{dy}{dx}_{(a, b)}$  of the function . so substitute x=4 and y=8 in dy/dx to find the slope of the tangent.

campbell_st · Answer

can I suggest the use of index laws for this problem before anything else

$$x^a \times a^b = x^{a + b}$$

so $$x \times x^{\frac{1}{2}} = x^{\frac{3}{2}}$$

it just eliminates the need for the product rule..

ash2326 · Answer

@jalotaibi Did you understand? Can you solve the rest of the problem?

anonymous · Answer

so i put 4 and 8 instead of x ? and then solve it ?

ash2326 · Answer

put x=4, we don't have a y in the equation, so we can't put y=8 anywhere
find dy/ dx value, it's the slope of your tangent

anonymous · Answer

if i put 4 the answer is 2.5

anonymous · Answer

that's the slope?

ash2326 · Answer

Check again, it's not 2.5

anonymous · Answer

3

ash2326 · Answer

Now you have slope of the tangent as 3 and it passes through the point (4, 8)
Can you write its equation?

anonymous · Answer

i get it the answer is 3x-4 ?