Question

Let f(x)=5+3/x

a) Find f′(x)

b)Find the slope of the tangent line at x=1. Slope = f′(1)=?

Answer #1

solution

f(x)=5+3/x

a) Find f′(x)

d(f(x)/dx = f'(x) = d(5)/dx + d(3/x)/dx

derivative of constant is zero = d(5)/dx =0

d(x^n) = nx^n-1 here n =-1

d(1/x) = d(x^-1) = -1x^(-1-1) = -1x^-2 = -1/x^2

d(1/x)/dx = -1/x^2

= d(5)/dx + 3d(1/x)/dx = 0 +3(-1/x^2) = -3/x^2

**d(f(x)/dx = f'(x) = d(5)/dx + d(3/x)/dx =
-3/x^2**

**derivative of a function f(x) is slope = d(f(x)/dx =
f'(x) = -3/x^2**

b)Find the slope of the tangent line at x=1. Slope = f′(1)=?

**derivative of a function f(x) is slope = d(f(x)/dx =
f'(x) = -3/x^2**

f'(1) put x =1

f'(1) = -3/(1^2) =-3

**Slope = f′(1)= -3**

find the equation of a tangent line(s) to the curve with slope 5
f(x)=x^3 + 3x^2 - 4x - 12
f'(x)= 3x^2 +6x - 4

. Find the slope of the tangent line to f-1 at the
point P(-1, 0) if f(x) = x+1/ x-1, and then find the
slope-intercept equation of the tangent line to the graph of
f-1 at P.

Let f(x)=22−x2f(x)=22-x2
The slope of the tangent line to the graph of f(x) at the point
(−4,6) is .
The equation of the tangent line to the graph of f(x) at (-4,6) is
y=mx+b for
m=
and
b=
Hint: the slope is given by the derivative at x=−4

Being f (x) = x^2 - 4x - 3, determine the slope of the line
tangent to the curve of
f (x) at the point where x =3.
VIII. Being f (x) = 5x^2 + 3x - 9, determine the slope of the
line tangent to the curve of
f (x) at the point where x = -1.
IX. Determine the equation of the line to the curve of f (x) =
x^2 - 9x , at the point where...

Suppose that ?(?)=−3?2−7. (A) Find the slope of the line tangent
to ?(?) at ?=−1. (B) Find the instantaneous rate of change of ?(?)
at ?=−1. (C) Find the equation of the line tangent to ?(?) at ?=−1.
?=

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...

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))

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.

find the slope then find the equation of a tangent line that is
tangent to the curve f(x)=x2tan(x) at (pi, 0) (hint: use
product rule)

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

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