differentiating question. (1 Viewer)

[girlworld_club]

y= ax^2 + bx + c passes through the point (1,6). The tangent there is parallel to the y axis whilst the tangent at x=3/4 is inclined at 45degrees to the x axis. Find the values of a,b, c.

This a 2 unit prelim question. any help or full working would be great.

 

[iBibah]

y= ax^2 + bx + c passes through the point (1,6). The tangent there is parallel to the y axis whilst the tangent at x=3/4 is inclined at 45degrees to the x axis. Find the values of a,b, c.

This a 2 unit prelim question. any help or full working would be great.

You sure that's not meant to be x-axis? Being parallel to the y-axis means the gradient there is undefined, and if this is a function, then the gradient will never be undefined.

 

[iBibah]

If it does mean x-axis, then differentiate f(x) to get 2ax+b.

Now f ' (1) = 0 (Equation 1)

and f ' (3/4) = 1 (tan45=m=1) (Equation 2)

Solve simultaneously for A and B.

Then to solve for c, solve for f(1) = 6.

 

[lolcakes52]

otherwise the equation has no solution.

 

[Leffife]

You sure that's not meant to be x-axis? Being parallel to the y-axis means the gradient there is undefined.

+1

I think she probably wrote it wrongly, but yes it MUST be parallel to the x-axis.