Calculus Jeopardy!

Differentiation

100

Differentiate: 

F(x)=3x+4

F'(x)=3

200

Find dy/dx:

y=4x²-3x+5

dy/dx=8x-3

300

The derivative of C(x)=-1/2x⁴+3/5x³-4x...

C'(x)=-2x³+9/5x²-4

400

Find y':

y=2x²-1/x+7

y'=4x+1/x²

500

Find dy/dx:

y= -2x³+2/x³

dy/dx=-6x²-6/x⁴

Tangents

100

If f'(x)=2x-4, find the gradient of the tangent at point (-3,2).

-10

200

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. 

300

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.

400

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

500

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

Normals

100

If f'(x) =1/2 at the point P(1,3), what is the gradient of the normal at point P?

-2

200

For y= 3x²-4x+5, what is the gradient of the normal at point Q(2,6)?

-1/8

300

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.

400

Find the equation of the normal to f(x) =3x+4 at (9.1).

y=-1/3x+4

500

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