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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
3
x
3
−
5
x
+
2
x
2
+
1
f(x)=\dfrac{3x^{3}-5x+2}{x^{2}+1}
f
(
x
)
=
x
2
+
1
3
x
3
−
5
x
+
2
. Answer the following. a. (i) Show that
f
(
x
)
f(x)
f
(
x
)
is differentiable for all real
x
x
x
. b. (ii) Find
f
′
(
x
)
f'(x)
f
′
(
x
)
. c. (iii) Calculate
f
′
(
1
)
f'(1)
f
′
(
1
)
. d. (iv) Hence write the equation of the tangent to the curve
y
=
f
(
x
)
y=f(x)
y
=
f
(
x
)
at the point where
x
=
1
x=1
x
=
1
.
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