Calculus Jeopardy!

Evaluate

100

g(x) = 6x² + 2x + 4

g'(3) = ?

g'(3) = 38

200

f(x) = sec(x) + cos(x)

f'(pi) = ?

f'(pi) = 0

300

h(x) = 2e^2x - 3^x

h'(2) = ?  

h'(2) = 208.51

400

g(x) = e^(4x - 5)3x

g'(4) = ?

g'(4) = 1.72

500

f(x) = cos(sin(x))

f'(pi/3) = ?

f'(pi/3) = -0.38

Derivatives

100

h(x) = 3x⁴ - cos(x)

h'(x) = 12x³ + sin(x)

200

f(x) = x^1/2 * 2tan(x)

f'(x) = x ^-1/2 * tan(x) + 2x^1/2 * sec²(x)

300

f(x) = 2x³ / sin(x)

f'(x) = (6x² * sin(x) - 2x³ * cos(x)) / sin²(x)

400

h(x) = e^(2x^1/2 + cos(x))

h'(x) = e^(2x^1/2 + cos(x)) * (x^-1/2 - sin(x))

500

g(x) = tan³(x² + 5x)

g'(x) = 3tan²(x²+5x)sec²(x²+5x)(2x+5)

Trig

100

Another way to write sec²(x)

(sec(x))² 

1/cos²(x)

1/(cos(x))² 

200

When looking at a given angle, what is opposite/adjacent?

tan(x) 

sin(x)/cos(x)

300

If one leg of a triangle is 5 and the other is 12, what is the length of the hypotenuse?

13

400

If one angle of a triangle is 72 and the adjacent side length is 5, what is the length of the opposite side?

15.39

500

If one angle of a triangle is pi/6 and the adjacent side length is 10, what is the length of the hypotenuse?

11.55

Eq of Tangent Lines

100

Equation of a tangent line at        (1, -8) 

f(x) = 7x² - 15x

y = -x - 7

200

Equation of a tangent line at x = 4

g(x) = 4x - 6x³ - 2x - (3/2)x² + 6x³ - 2x 

y = -12x + 24

300

Equation of a tangent line at      y = 0

y = (x² - 4)/(x - 2) + 2

y = 1

400

Equation of a tangent line at          x = pi/4

f(x) = cos(4x) + sin(2x) + tan(x)

y = 2x + 1 - pi/2

y = 2x - 0.57

500

Equation of a tangent line at the point (0, y)

f(x)  = (4x + 16)^1/2 + (4x + 2)² 

y = 33/2x + 8

y = 16.5x + 8