Question

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

Answer #1

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For what values of c is there a straight line that intersects
the curve y = x4 + cx3 + 12x2 − 7x
+ 4 in four distinct points? (Enter your answer using interval
notation)

For the curve f(x) = 2x 3 − 9x 2 + 12x − 5, find (i) the local
maximum and minimum values, (ii), the intervals on which f is
increasing or decreasing, and (iii) the intervals of concavity and
the inflection points.

The
plane y+z=2 intersects the ‘funky’ cylinder x^2 + y^4 =17 in a
curve C.
A) Find a parametric equation of the tangent line to C at the
point (4,1,1)
B) How was the direction vector found in part A and how do you
know its the right direction?

Which of the following has the most critical values?
xe^(2x)
4x^3-9x^2-12x+3
4^(4/5) * (x-2)^2
|x^2-1|

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.

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

Please show work
1. Find the first derivate
a). y= In(2x+5/4x-8)
b). y= xe^x+1
c). y= xln(x+1)
d). y= (x/lnx)
2. Find the critical points. Write the coordinates (x,y)
a). f(x)= 3x^2/3 - 2x
b). f(x)= 2x^3 + 3x^2 - 12x
c). f(x)= x √x+3
d). f(x)= (lnx/ x^2)

3. Find the equation of the tangent line to the curve 2x^3 + y^2
= xy at the point (−1, 1).
4. Use implicit differentiation to find y' for sin(xy^2 ) − x^3
= 4x + 2y.
5. Use logarithmic differentiation to find y' for y = e^4x
cos(2x) / (x−1)^4 .
6. Show that d/dx (tan (x)) = sec^2 (x) using only your
knowledge of the derivatives of sine/cosine with derivative
rules.
7. Use implicit differentiation to show that...

1)
Find the equation of the line that psses through the vertex if the
parabola f(x)=2x^2-12x+19 and that crosses the x-axis at x=5
2) Find the equation of the line that passes through the
certex of the parabala f(x)=3x^2-12x+17 and has y-intercept of
(0,10)

The line that is normal to the curve X^2+XY-2y^2=0 at (2,2)
intersects the curve what other point

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