find tangent line as directed to the curve y = x^4-14x^2+17x+40 perpendicular to the line x-7y = 4
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Answer:
The equation of the tangent is
y
=
7
x
−
5
Explanation:
let
f
(
x
)
=
x
4
+
2
x
2
−
x
Then the derivative is
f
'
(
x
)
=
4
x
3
+
4
x
−
1
At the point
(
1
,
2
)
,
f
'
(
1
)
=
4
+
4
−
1
=
7
So the slope of the tangent is
m
=
7
The equation of the line is,
y
−
2
=
7
(
x
−
1
)
y
−
7
x
=
−
5
graph{(y-x^4-2x^2+x)(y-7x+5)=0 [-5.55, 5.55, -2.773, 2.776]}
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