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Point A lies on the curve y=3x^2+5x+2. The x-coordinate of A is 2. Find the equation of the tangent to the curve at the point A

First differentiate the function with respect to x, dy/dx=6x+5 this finds the gradient function now calculate the gradient at point A by inputing x=2 into the gradient function 6(2)+5=17. Now using y=mx+c wh...
DS
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Find the tangent to the equation y=x^2 -2x +4 when x=2

When X=2 Y=2^2-2(2)+4=4 So the coordinates are (2,4)Differentiate Y so dy/dx = 2x-2Tangent Gradient when x=2 is 2(2)-2=2 so m=2We need to find the y intercept to get out tangent equationso y=2x+c , we sub in...
NN
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y=(6x^9 +x^8)/(2x^4), work out the value of d^2y/dx^2 when x=0.5

The question can be represented by the notation d 2 y/dx 2 |x=0.5 , meaning the second derivative of y with respect to x resolved at x=0.5. Since y is in the form f(x)/g(x), the quotient rule could be used, ...
OC
5402 Views

y = (x+4)(6x-7). By differentiating, find the x coordinate of the maximum of this equation.

y=(x+4)(6x-7)y=6x 2 +17x-28dy\dx = 12x + 17To find the x coordinate of the stationary points of y, let dy\dx=012x+17=0x=-17\12
AS
2262 Views

Why does the discriminant b^2-4ac determine the number of roots of the quadratic equation ax^2+bx+c=0?

The rule for the discriminant: if b^2-4ac>0 then the quadratic has two roots if b^2-4ac=0 then the quadratic has one root if b^2-4ac<0 then the quadratic has no rootsRecall that the formula for solving...
DG
9767 Views