Vertical tangent lines If a function ƒ is continuous at a andlimx-a 0 ƒ′(x) 0 = ∞, then the curve y = ƒ(x) has a vertical tangent lineat a, and the equation of the tangent line is x = a. If a is an endpoint ofa domain, then the appropriate one-sided derivative is used. Use this information to answer the following questions 75. Verify that ƒ(x) = x1/3has a vertical tangent line at x = 0.
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:
Vertical tangent lines If a function ƒ is continuous at a and
limx-a 0 ƒ′(x) 0 = ∞, then the curve y = ƒ(x) has a vertical tangent line
at a, and the equation of the tangent line is x = a. If a is an endpoint of
a domain, then the appropriate one-sided derivative
is used. Use this information to answer the following questions 75. Verify that ƒ(x) = x1/3
has a vertical tangent line at x = 0.
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