the diagram shows the curve y = (x-2)² + 1 with minimum point P. The point Q on the curve is such that the gradient of PQ is 2. Find the area of the region shaded in the diagram between PQ and the curve.
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Answer :
First we will find ∫'(x), ehich is derivative of ∫(x).
∫'(x) = 2x - 0 = 2x
Second, substitute in the value of x, in this case x = 1
∫'(1) = 2(1)
The slope of the curve y = (x - 2)² at the x value of 1 is 2.
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Step-by-step explanation:
The slope of a curve of
y
=
f
(
x
)
at
x
=
a
is
f
'
(
a
)
.
Let us find the slope of
f
(
x
)
=
x
3
−
x
+
2
at
x
=
1
.
By taking the derivative,
f
'
(
x
)
=
3
x
2
−
1
By plugging in
x
=
1
,
f
'
(
1
)
=
3
(
1
)
2
−
1
=
2
Hence, the slope is
2
.
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