Question

Find the slope of the secant lines over the specified intervals for
the functions f(x)= -1/2x^2+2x .

a) [2,3]

b) [2,2.1]

c) Estimate the slope of the tangent line at x=2

d) Use your estimate to find the equation of the tangent line
at x=2

Answer #1

refer to the graph of y=f(x)=x^2+x shown
a. Find the slope of the secant line joining(-3,f(-3)) and
(0,f(0))
b. Find the slope of the secant line joining (-3,f(-3))
and(-3+h,f(-3+h))
c . Find the slope of the graph at (-3,f(-3))
d. Find the equation of the tangent line to the graph at
(-3,f(-3))

Let f(x) = x^3 - x
a) Find the equation of the secant line through (0,f(0)) and
(2,f(2))
b) State the Mean-Value Theorem and show that there is only one
number c in the interval that satisfies the conclusion of the
Mean-Value Theorem for the secant line in part a
c) Find the equation of the tangent line to the graph of f at point
(c,f(c)).
d) Graph the secant line in part (a) and the tangent line in part...

Consider the function f(x) = √x and
the point P(4,2) on the graph f.
a)Graph f and the secant lines passing through the
point P(4, 2) and Q(x,
f(x)) for x-values of 3, 5, and 8.
b) Find the slope of each secant line. (Round your answers to
three decimal places.)
(line passing through Q(3, f(x)))
(line passing through Q(5, f(x)))
(line passing through Q(8, f(x)))
c)Use the results of part (b) to estimate the slope of the
tangent line...

f(x) = 4x^2-5x+6
a) Find the slope in between where x=2 and x=3
b) Find the slope in between where x=3 and x=4
c) Find the slope in between where x=3 and x=a
d) Find the slope in between where x=3 and x=3+h
e) Use the answer in part c to find the slope of the line
tangent to f(x) at x=3
f) Use the answer in part d to find the slope of the line
tangent to f(x) at...

Find fhe equation of the tangent lines with slope of 5
a) f(x)= x^3 + 3x^2 - 4x -12
b) g(x)= 3x^2 + 6x - 4

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!

Find the derivative of f(x) - In(2x)
1. what point on the graph of f(x) at which the tangent line is
horizontal?
2. what point on the graph of f(x) at which the tangent is
vertical?
3. is there a point on the graph f(x) at which the tangent has a
slope 1?

PROBLEM: Given f(x)=4x - x2 + k & (1,3+k) on the
graph of f.
(K=3)
a) Write your equation after substituting in the value of k.
(K=3)
b) Calculate the function values, showing your calculations,
then graph three secant lines
i. One thru P(1,f(1)) to P1(0.5,__)
ii. One thru P(1,f(1)) to P2(1.5,__)
iii. One thru P1 to
P2
c) Find the slope of each of these three secant lines showing
all
calculations.
d) NO DERIVATIVES ALLOWED HERE! Use the...

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.

i) Given that
5x3-2x+y=2, find the value of
at x=1.
ii) Determine the
slope of the tangent line to the curve
y=lnx2 at
x=e2 is . . .
iii) Given that
fx=x+sinx2, find
f'(x).

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