Can someone please explain how to do a problem like:

Write and equation of the line that is tangent to the graph of the function y=f(x) at the point P with the given x-coordinate.

f(x)= 10(1-(x/10))^2, x = 15.

Also, can you use point slope form to explain? I never learned point slope form I always used y=mx+b so point slope is a little foreign to me.

Question

Can someone please explain how to do a problem like: 

Write and equation of the line that is tangent to the graph of the function y=f(x) at the point P with the given x-coordinate. 

f(x)= 10(1-(x/10))^2,   x = 15.

Also, can you use point slope form to explain? I never learned point slope form I always used y=mx+b so point slope is a little foreign to me.

ribhu · Answer

u have to differentiate the function first of all

ribhu · Answer

as the derivative at the required point on the curve is the slope of the tangent drawn to that curve.

ribhu · Answer

@tjb69812 u there?

anonymous · Answer

Yessir sorry

ribhu · Answer

u got what i wrote?

anonymous · Answer

Yes, let me take the derivative really fast to catch up

ribhu · Answer

you are given a x coordinate so putting x in the function will give you a y coordinate, now you have a point on the curve, and you know the slope of the tangent to be drawn which is nothing but the derivative of the curve at a given x

ribhu · Answer

this becomes simple equation of line with point and slope known.

anonymous · Answer

20(1-(x-10))*(-1/10), right? Or did I screw that up hahah

ribhu · Answer

let the point on the curve be (x1,y1) then the equation becomes: |dw:1425356526553:dw|