For the given function f and values of a and b, find the slope of the secant line between the points (a, f(a)) and (b, f(b)):
f(x) = x2, a = 1, b = 2.
Answer
f(x) = x2, a = 1, b = 2, f(a) = 1, f(b) = 4,
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f(x) = x2, a = 1, b = 1.5.
f(x) = x2, a = 1, b = 1.5, f(a) = 1, f(b) = 2.25,
f(x) = sin(x), a = 0, b = π/2.
f(x) = sin(x), a = 0, b = π/2, f(a) = 0, f(b) = 1,
f(x) = x3 – 2x + 3, a = 1, b = 4.
f(x) = x3 – 2x + 3, a = 1, b = 4, f(a) = 2, f(b) = 59,
For the given function f and values of a and b, what is the slope of the secant line between the points (a, f(a)) and (b, f(b))?
f(x) = x4 – 2, a = -2, b = 2.
With f(x) = x4, a = -2, b = 2, f(a) = 16, f(b) = 16,
Given the values of a and b, what must h be so that a + h = b?
a = 4, b = 4.25.
h = 0.25 since we need to add 0.25 to a = 4 to find b = 4.25.
a = -1, b = -1.5.
h = -0.5 since we need to subtract 0.5 from a = -1 to find b = -1.5.
For the given function f, value of a, and value of h, what is the slope of the secant line between (a, f(a)) and (a + h, f(a + h))?
f(x) = x2, a = 1, h = 0.1.
With f(x) = x2, a = 1, h = 0.1,
a + h = 1.1, f(a) = 1, f(a +h) = 1.21.
So
For the given function f, value of a, and value of h, what's the slope of the secant line between (a, f(a)) and (a + h, f(a + h))?
f(x) = 1 – x2, a = 0, h = 0.1.
With f(x) = 1 – x2, a = 0, h = 0.1,
a + h = 0.1, f(a) = 1, f(a +h) = 0.99.
f(x) = cos(x), a = 0, h = -π/2.
We're given f(x) = cos(x), a = 0, and h = -π/2,
so
a + h = -π/2, f(a) = 1, f(a + h) = 0,
and
f(x) = x3– x, a = 1, h = 4.
We have f(x) = x3 – x, a = 1, and h = 4, so
a + h = 5, f(a) = 0, and f(a + h) = 120.
The slope is
f(x) = 3x, a = -2,and h = -0.2.
With f(x) = 3x, a = -2, h = -0.2, we have
a + h = -2.2, f(a) = -6, f(a + h) = -6.6, so
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