Finding Derivatives
Find dy/dx of y=9x
What is 9?
If f(x)=2x2-2x+5
Find f'(x) of f'(1)
What is f'(1)=2?
Find an equation for the line that is tangent to the curve y=5x3-5x at the point (1,0)
What is y=10x-10?
For the function, find the points on the graph at which the tangent line is horizontal.
y=x2-4
What is (0,-4)?
Use the derivative to help show whether the function is always increasing, decreasing, or neither
f(x)=x3+2x
What is f'(x)=3x2+2?
Find dy/dx of -4x4
What is -16x3
If f(x)=2x2-4x+8
find f'(2)
What is f'(2)=4?
Find an equation for the line that is tangent to the curve y=3x3-3x at the point (-1,0)
What is 6x+6?
For what point of the curve of y=5x-6x is the slope of a tangent line equal to 4?
What is (1,-1)?
The equation R(v)= 6200/v can be used to determine the heart rate, R, of a person whose heart pumps 6200 mL of blood per minute and v mL of blood per beat.
Find the change in heart with respect to v, the output per beat
Find the rate of change at v=60mL per beat
what is R'(v)=-6200/v2? AND what is -1.72 beat/min per mL
Differentiate y=2√(x)
What is 1/(√(x))?
If y=8x+(8/x8)
find dy/dx at x=1
What -56?
Find the equation of the tangent line to the graph of 1/(x4) at (1,1)
What is y-1=-4(x-1)?
OR
What is y=-4x
For the function, find the point(s) on the graph at which the tangent line has a slope of 4
y=(1/3)x3-2x2+7x+13
What is (3,25), (1,55/3)?
In t years, the population of a certain city grows from 800,000 to a size P given by P(t)=800,000+500t2.
Find the growth rate, dP/dt
Find the population after 10 years
What is 10,000t? AND What is 1,300,000
Find f'(x). f(x)= 8/(3x4)
What is f'(x)=-32/3x5?
If y=1/(7x4)
find dy/dx at x=1
What is -4/7?
Find an equation of the line tangent to the graph of f(x)=1/(x5) at (2,1/(32))
What is y-(1/32)=-(5/64)(x-2)?
For the function, find the point(s) on the graph at which the tangent line has a slope of 10
y=-0.025x2+9x
What is (-20,-190)
Find dy/dx. The function can be differentiated using theorems developed in this section if some algebra is performed beforehand.
y=(x+9)3
What is dy/dx= 3x2+54x+243
Find the derivative of the following function
f(x)= 7x-3/4+6x-1/2+x7-3
What is (-21/2)x-7/4-3x-3/2+7x6?
If y= 1/(5x12)
find dy/dx at x=1
what is -12/5?
Find an equation of the line tangent to the graph if f(x)=1/(x2) at (-3, 1/9)?
What is y-1/9=2/27(x+3)?
For the function find the point(s) on the graph at which the tangent line is horizontal
y=x3-8x2+16x+6
What is (4/3,418/27), (4,6)?
The view V, or distance in miles, that one can see to the horizon from a height h, in feet, is given by V=1.18√h
Find the rate of change with respect to h
How far can one see to the horizon from an airplane at a height of 40,000 ft
What is 0.59/√h? AND What is 236 miles