Calculus Answers

Equation of a Tangent Line: Find the standard (slope-intercept form) equation of the tangent line to the following functions at the specified points. (Show your complete solution, use Method 1)

1. 𝑓(𝑥) = 𝑥² − 4𝑥+1 at point (0,1)
2. 𝑓(𝑥) = 𝑥³+ 2 at point (1,3)
3. 𝑓(𝑥) = 2𝑥⁴+ 3𝑥³ − 2𝑥 + 7 at point (-1,8)
4. 𝑓(𝑥) = √2𝑥 + 7 𝑎𝑡 𝑥 =1

Air is pumped into a spherical balloon at the rate of 100 cm3/s. How fast is the diameter increasing when the diameter is 10 cm? 

The slope of f(x)=x³−12x²+36x−48 is zero at which value/s of x?

What is the slope of y=2x³ +3x²−3x−2 at x=1?

The slope of the curve y=3x²−5 at point (−1,−2) is

Using polar coordinates find if the limit does or does not exist for

Lim(x,y)approaches(0,0) (2x/(x^2+X+y^2))

Trace the curve 𝑦 = 8/4-x^2 , and state all the properties you use to trace it. 

Determine the area of the given curves

1 . 𝑦² = 2 𝑥 ; 𝑦 = 𝑥 − 4

2. 𝑦 = 𝑥 − 𝑥² ; 𝑦 = − 𝑥

Find the lengths of the sides of an isosceles triangle with a given perimeter if its area is to be as great as possible.

A rectangular field is to be enclosed and divided into four equal lots by fences parallel to one of the sides. a total of 10,000 meters of fence are available. Find the area of the largest field that can be enclosed.