How do I solve this maths question?

Question

a curve has the equation y= (1+x)(4-x)
the first part asks what the x coordinates of the the points where the curve crosses the x axis are and I pense that they are -1 and 4 but please correct me if i am wrong.
then it asks me to find the x coordinate of maximum point (M) of the curve.
Ic ould do this if it was like y= x^2+4 but the fact that it is (1+x)(4-x) or y=x^2+3x+4 is totally confuzling me!

Gandalf · Accepted Answer

Adding to Brian's answer, the derivative of a function  y = f(x) represents the rate of change of y with respect to x.  At the exact maximum or minimum of a such a function the rate of change = zero.  So the derivative f'(x) can be set equal to zero to solve for x at that point.  Neil's answer matches because the function is symmetrical about the maximum point.  If it were not, his method would not work.  Brian's method is correct regardless of the function's symmetry or lack thereof.

Anonymous · Answer

I assume this is a Calculus question, because that is how I shall answer it.  Taking f(x) = (1+x)(4-x) = -x^2+3x+4, the derivative f'(x) is -2x+3.  Solving f'(x)=0, you get x to be 1.5.  If you test that out with f(x), f(1.5) is 6.25.  If you graph both equations – f(x) and f'(x) – you can check.  May I recommend if you don't have it...

http://www.graphcalc.com/ 

If you are not taking a Calculus class... um... I don't know!

Neil D · Answer

The roots that cross the x axis are correct -1 and 4

To find turning point:  x= (-1+4)/2 =1.5

Then sub x= 1.5 into equation to find y coordinate

Y=1.5^2 + 3(1.5) + 4
 =2.25 + 4.5 + 4
= 10.75

So coordinates are (1.5,10.75)

I think thats itlol

How do I solve this maths question?

3 Answers