Derivatives
5
Simplify log base ten of one hundred.
2
* triple points *
2 + 1
3
What is the purpose of the chain rule?
The chain rule is used when a function is inside another function. It helps us differentiate composite functions by multiplying the derivative of the outer function by the derivative of the inner function.
* double points *
How do negative exponents work?
Negative exponents represent reciprocals of the base, meaning the value becomes smaller as the exponent becomes more negative.
When is differentiation not possible?
Differentiation is not possible when a function is discontinuous, has a sharp corner, or has a vertical tangent, because the rate of change is undefined in those cases.
What is two power five?
32
What is log base ten of ten?
1
* double points *
What is the definition of an asymptote?
a line that a curve approaches arbitrarily closely but never actually touches or intersects at a finite distance
Define what a derivative is
A derivative tells us the rate of change of a function. It describes how quickly the output of a function changes when the input changes.
What is an example of an exponential in the real world?
e.g. Finance, population studies, radioactive decay, medicine dosage, and computer science growth models.
Why are logarithms useful?
Logarithms are useful for solving equations with exponents and for measuring growth on a large scale, like earthquakes or sound.
What is two squared?
Double two, three times.
Two doubled once is four, doubled again is eight, doubled again is sixteen.
Which functions have zero derivatives?
Functions that are constant, meaning they do not change with respect to the input, have zero derivatives everywhere.
what is an exponential function?
An exponential function is a function where a constant base is raised to a variable exponent, describing rapid growth or decay.
What is log base two of eight?
3
A parabola has its axis of symmetry on the x-axis. Explain how you could find the turning point using symmetry or algebra.
Because the axis of symmetry lies along the horizontal axis, the turning point occurs at the midpoint between any pair of points with the same height. Algebraically, complete the square or use the average of the intercepts to locate the turning point horizontally, then substitute to find its height.