Find the equation of tangent line to the curve when y is equal to x cube minus 3 x + 5 at the point (2,7)
Answers
Answer:
First, let's find the value of
y
for
(
3
,
y
)
to be on the graph of the function.
y
=
3
(
3
)
2
−
5
(
3
)
+
2
y
=
27
−
15
+
2
y
=
14
Next, differentiate using the power rule. Let your function be
f
(
x
)
, then:
f
'
(
x
)
=
6
x
−
5
Now, plugging in our value of x to find the slope:
f
'
(
3
)
=
6
(
3
)
−
5
f
'
(
3
)
=
13
∴
The slope of the tangent is
13
. Now we know a point on the original function
(
3
,
14
)
and the slope of the tangent, 13.
We will use point slope form to determine the equation of the tangent.
y
−
y
1
=
m
(
x
−
x
1
)
y
−
14
=
13
(
x
−
3
)
y
−
14
=
13
x
−
39
y
=
13
x
−
25
∴
The equation of the tangent is
y
=
13
x
−
25
.
Hopefully
Step-by-step explanation:
please mark the brainliest
Step-by-step explanation:
slope of tangent = dy/dx = d(x^3-3x-5)/dx = 3x-3
Now put the value of x=2 then slope of tan become 9 Now find the equation of tangent to curve (y-y') = slope of tangent (x-x') (y-7) = 9(x-2) therefore equation of tangent to curve is 9x-y-11=0