Calculus derivative question (1 Viewer)

[enigma_1]

The curve y = ax^2 + bx + c touches the line y = 2x at the origin and has a maximum
point when x = 1. Find the values of a, b and c.


ANSWER
a=-1, b=2 c=0

 

[bottleofyarn]

The curve y = ax^2 + bx + c touches the line y = 2x at the origin and has a maximum
point when x = 1. Find the values of a, b and c.


ANSWER
a=-1, b=2 c=0

First off, I would sub in the point given (the origin).
Next, you differentiate and realise that y = 2x is the tangent at x = 0
Then, use the fact that the maximum turning point is at x = 1.

In these questions, make sure you use all the information provided - one for each variable you have to find.

 

[braintic]

The equation must be of the form y=A(x-1)^2 +B

Differentiate: y' = 2A(x-1)

At x=0, y'=2: 2=-2A; A=-1

Sub (0,0) into original: A+B=0; B=1

y=-(x-1)^2 +1

y=-x^2 +2x
ie. a=-1, b=2

 

[enigma_1]

Thanks a tonne guys!