Tangent lines Assume ƒ and g are differentiable on their domainswith h(x) = ƒ(g(x)). Suppose the equation of the line tangent tothe graph of g at the point (4, 7) is y = 3x - 5 and the equationof the line tangent to the graph of ƒ at (7, 9) is y = -2x + 23.a. Calculate h(4) and h′(4).b. Determine an equation of the line tangent to the graph of h at(4, h(4))
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Tangent lines Assume ƒ and g are differentiable on their domains
with h(x) = ƒ(g(x)). Suppose the equation of the line tangent to
the graph of g at the point (4, 7) is y = 3x - 5 and the equation
of the line tangent to the graph of ƒ at (7, 9) is y = -2x + 23.
a. Calculate h(4) and h′(4).
b. Determine an equation of the line tangent to the graph of h at(4, h(4))
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