Thread: 2 calculus problems

1) Find the equation of the tangent to f(x)=(2x-1)^3 where x=1

2) Suppose that for a compant manufacturing calculators, the cost, revenue, and profit equations are given by C=90,000+30x R=300x - (x^2)/30 & P=R-C where the production output in 1 week is x calculators. if production is increasing at a rate of 500 calculators per week, when production output is 6,000 calculators, find the rate of increase (decrease) in: a) cost b) revenue, c) profit.

Any help would be greatly appreciated.
Thanks!

Originally Posted by salu34

1) Find the equation of the tangent to f(x)=(2x-1)^3 where x=1

2) Suppose that for a compant manufacturing calculators, the cost, revenue, and profit equations are given by C=90,000+30x R=300x - (x^2)/30 & P=R-C where the production output in 1 week is x calculators. if production is increasing at a rate of 500 calculators per week, when production output is 6,000 calculators, find the rate of increase (decrease) in: a) cost b) revenue, c) profit.

Any help would be greatly appreciated.
Thanks!

I'll help you with the first question...

Find the derivative of f(x):



The slope is the rate of change at a given point, (i.e. it's derivative).



Now, what is the y-coordinate for x=1?



Use the slope-intercept form for a line:



Plug and chug...

how did you find that the derivative of 6(2x-1)^2 was 6?

Originally Posted by salu34

how did you find that the derivative of 6(2x-1)^2 was 6?

colby2152 substituted into the differentiated function.