Question

Let L(x) be the tangent to the curve f(x) = x^ 4−2x ^2−x at x = 2. Find the points where L(x) intersects the curve again.

Answer #1

1. Let f(x)=(x^2+1)(2x-3)
Find the equation of the line tangent to the graph of f(x) at
x=3.
Find the value(s) of x where the tangent line is horizontal.
2. The total sales S of a video game t months after being
introduced is given by the function
S(t)=(5e^x)/(2+e^x )
Find S(10) and S'(10). What do these values represent in terms
of sales?
Use these results to estimate the total sales at t=11 months
after the games release.

f(x)=3x^4-7x^2+2x+1
Find the tangent line at x=2

1.) Find the equation of the tangent line to the graph of the
function f(x)=5x-4/2x+2 at the point where x=2
2.) Find the derivative: r(t)=(ln(t^3+1))^2

Find equations of the tangent lines to the curve f (x) = (2x
+1)/(4x-3) that are perpendicular to the line 5x−2y+2=0.
Explanation would be appreciated!

1. Let f(x)=−x^2+13x+4
a.Find the derivative f '(x)
b. Find f '(−3)
2. Let f(x)=2x^2−4x+7/5x^2+5x−9, evaluate f '(x) at x=3 rounded
to 2 decimal places.
f '(3)=
3. Let f(x)=(x^3+4x+2)(160−5x) find f ′(x).
f '(x)=
4. Find the derivative of the function f(x)=√x−5/x^4
f '(x)=
5. Find the derivative of the function f(x)=2x−5/3x−3
f '(x)=
6. Find the derivative of the function
g(x)=(x^4−5x^2+5x+4)(x^3−4x^2−1). You do not have to simplify your
answer.
g '(x)=
7. Let f(x)=(−x^2+x+3)^5
a. Find the derivative....

Find the equation of the tangent to the curve y= x sqr(2x^2+7)
at x=3

Q1. (a) Find the equation of the tangent to the curve
f(x)=x^2+4x+2 at the point where the gradient is 8.
(b) Find the equation of the normal at this point, where normal
gradient times tangent gradient is -1.

Let f(x)=2x^3 - 9x^2 +12x -4
Find the intervals of which f is increasing or decreasing
Find the local maximum and minimum values of f
Find the intervals of concavity and the inflection points

let S be the surface defined by x^4-2x^2y^2+3z^2=12, Find the
equation of the tangent plane to the surface S at (0,1,2).

For what values of c is there a straight line that intersects
the curve y=x^4+cx^3+12x^2-2x+8 in 4 distinct points? answer in
interval notation

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