Higher Maths Differentiation Help?

First of all you need to find out what the full equation is by subbing in the point (3,9), if you forget to do this then you will get the answer (4,0):

9 = (3 - 4)² + k

k = 8

y = x² - 8x + 24

When you differentiate you end up with a formula that gives the the gradient of the original line.

A stationary point is a turning point on a graph ie. it is when the gradient is equal to 0.

So to answer this question you need to differentiate the equation and then make it equal to 0.

To differentiate, multiply by the original power and then take one off the power:

y = x² - 8x + 24

dy/dx = 2x - 8

Now make it equal to 0 to find x:

2x = 8

x = 4

Now sub 4 back into the original equation to find out what y is:

4² - (8 x 4) + 24 = y = 8

So the answer is A) (4,8)

first find k

(3,9) => 9 = (3-4)^2 +k

=> k = 8

dy/dx = 2(x-4) x 1 = 2(x-4)

gradient at turning point is 0 so 2x - 8 = 0 so x is 4

now substitue x into the equation y = (4-4)^2 + 8 => y=8

so turning point is (4,8)

y(3)=9 gives 9=(3-4)²+k→k==8.

So y=(x-4)²+8, dy/dx=2(x-4)=0

for a stationary point, and x=4,

y=8. The answer is A).

whilst the tangent is parallel to the x-axis, it skill that the tangent has a slope of 0 y = 2x^3 - 3x^2 - 12x + 12 dy/dx = 6x^2 - 6x - 12 dy/dx = 0 0 = 6x^2 - 6x - 12 0 = x^2 - x - 2 x = (a million +/- sqrt(a million + 8)) / 2 x = (a million +/- 3) / 2 x = -2/2 , 4/2 x = -a million , 2 y = 2x^3 - 3x^2 - 12x + 12 y = -2 - 3 + 12 + 12 , sixteen - 12 - 24 + 12 y = -5 + 24 , 28 - 36 y = 19 , -8 (-a million , 19) , (2 , -8)

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