Find the polynomial f ( t ) of degree 3 such that f ( 1 ) = 1 , f ( 2 ) = 5 , f ′ ( 1 ) = 2 , and f ′ ( 2 ) = 9 , where f ′ ( t ) is the derivative of f ( t ) . Graph this polynomial.
Find the polynomial f ( t ) of degree 3 such that f ( 1 ) = 1 , f ( 2 ) = 5 , f ′ ( 1 ) = 2 , and f ′ ( 2 ) = 9 , where f ′ ( t ) is the derivative of f ( t ) . Graph this polynomial.
Solution Summary: The author explains how to find the polynomial f(t) of degree 3 and draw a graph for it.
Find the polynomial
f
(
t
)
of degree 3 such that
f
(
1
)
=
1
,
f
(
2
)
=
5
,
f
′
(
1
)
=
2
, and
f
′
(
2
)
=
9
, where
f
′
(
t
)
is the derivative of
f
(
t
)
. Graph this polynomial.
A) find the inflection point ( x and y value) of the graph of f
Find the derivative of the function:
f(x)
17
16
0-17
17
4
0-17
16
=
2x – 7
3x – 2
-
at x = 2
2. Consider the function f(x) = 4 – x².
(a) Draw a sketch of the graph of the function.
(b) Find the slope of the secant line connecting the points P(1, 3) and Q(2,0) on the
graph.
(c) Find the slope of the secant line connecting the points P(1,3) and Q(x,4 – x²).
(d) Use algebra to simplify your formula from part (c) as much as possible, assuming
that P and Q are distinct points.
(e) What value do you get when you plug x = 1 into the simplified expression you found
in part (d)?
(f) Assume that your answer in part (e) is the slope of the tangent line to the graph
y = 4 – x2 at the point P(1,3). Use that information to write an equation for the
tangent line to the graph y = 4 – a² at the point P(1,3).
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