Differentiation
Differentiate:
F(x)=3x+4
F'(x)=3
If f'(x)=2x-4, find the gradient of the tangent at point (-3,2).
-10
If f'(x) =1/2 at the point P(1,3), what is the gradient of the normal at point P?
-2
Find dy/dx:
y=4x2-3x+5
dy/dx=8x-3
The gradient of a curve at point (-1,5) is zero. What can you say about this point?
(-1,5) is a turning point.
Or (-1,5) is a local max or local min.
For y= 3x2-4x+5, what is the gradient of the normal at point Q(2,6)?
-1/8
The derivative of C(x)=-1/2x4+3/5x3-4x...
C'(x)=-2x3+9/5x2-4
If f'(x0>0 for -2<x<5, and f'(x)<0 for 5<x, what can you say about f(x) at x=5?
There is a local maximum at x=5.
If the gradient of the normal is undefined at x=-5 for some curve g(x), what can you say about the curve at x=-5?
The curve has a local min or max at x=-5 because the slope of the tangent would be 0.
Find y':
y=2x2-1/x+7
y'=4x+1/x2
Consider f(x)=x2-5x+6. Find the equation of the tangent line at (3,0). Give your answer in the form y=mx+b.
y=x-3
Find the equation of the normal to f(x) =3x+4 at (9.1).
y=-1/3x+4
Find dy/dx:
y= -2x3+2/x3
dy/dx=-6x2-6/x4
For the function y=-2x2+3x-5, Find the equation of the tangent line at x=-2. Give your answer in the form y=mx+b.
y=11x+3
The equation of the normal to y=1/2x4-2/x2 at point A(1,3). Give your answer in the form ax+by+c=0
0=-1x-6y+114