What is the alternate derivative formula?

\lim_{x\to a}\frac{f\left(x\right)-f\left(a\right)}{x-a}

identify the function and the value for c of: \lim_{h\to0}\sqrt{h+25}-5

f\left(x\right)=\sqrt{x} and c= 25

Which of the following represents the derivative formula?

f'\left(x\right)=\frac{\lim}{h→0}\frac{f\left(x+h\right)-f(x)}{h}

set up the alternative derivative equation with the equation f\left(x\right)=3x+7 and a=4

\lim_{x\to4}\frac{3x+7-19}{x-4}

identify the function and the value for c: \lim_{x\to4}\frac{\left(x^2-x+3\right)^2-225}{x-4}

f\left(x\right)=\left(x^2-x+3\right)^2 and c=4

What is a Tangent line?

a straight line that touches a function at only one point.

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calculus derivatives

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Answers

1
Which formula gives you the slope of a tangent line?
The difference qoutient
the opposite reciproca of the slope of the normal line
the alternate derivative formula
all of the above
2
What is the alternate derivative formula?
\lim_{x\to0}\frac{f\left(x+h\right)-f\left(a\right)}{h}
\lim_{x\to0}\frac{f\left(x\right)-f\left(a\right)}{x-a}
\lim_{x\to a}\frac{f\left(x+h\right)-f\left(a\right)}{x-a}
\lim_{x\to a}\frac{f\left(x\right)-f\left(a\right)}{x-a}
3
given y=x^2-x+2 use the deffinition of derivitive to find f'(x)
x
2x
2x + h^2
x+h^2
4
Find the slope of the tangent line using the alternate derivitive formula if f\left(x\right)=\sqrt{2x+2} at x=1
m=1
m=\frac{1}{2}
m=-1
m=2
5
Indian Mathematicians created zero and made it the meaning of Nothing.
False
True
6
Format for a tangent line?
y'=tan(x)
y – y1 = m(x – x1)
y=mx+b
y'=cos(x)
7
identify the function and the value for c of: \lim_{h\to0}\sqrt{h+25}-5
f\left(x\right)=\sqrt{x} and c = 5
f\left(x\right)=\sqrt{x+25} and c = 5
f\left(x\right)=\sqrt{x+25} and c=25
f\left(x\right)=\sqrt{x} and c= 25
8
Which of the following represents the derivative formula?
f'\left(x\right)=\frac{\lim}{x→0}\frac{f\left(x-h\right)-f(x)}{h}
f'\left(x\right)=\frac{\lim}{h→0}\frac{f\left(x+h\right)-f(x)}{h}
f'\left(x\right)=\frac{\lim}{x→0}\frac{f\left(x+h\right)-f(x)}{h}
f'(x)=\frac{\lim}{h→0}\frac{f\left(x-h\right)-f\left(x\right)}{h}
9
If m=5 and the point is (3,4) What is the equation of the tangent line?
y=5(x+3)-4
y=5(x-3)+4
y=3(x-5)-4
10
set up the alternative derivative equation with the equation f\left(x\right)=3x+7 and a=4
\lim_{x\to4}\frac{3x+7}{x-4}
\lim_{x\to4}\frac{3x+7-19}{x-4}
\lim_{x\to4}\frac{3x+7-4}{x-4}
\lim_{x\to0}\frac{3x+7-19}{x-4}
11
identify the function and the value for c: \lim_{x\to4}\frac{\left(x^2-x+3\right)^2-225}{x-4}
f\left(x\right)=\left(x^2-x\right)^{ } and c=3
f\left(x\right)=\left(x^2-x+3\right)^2 and c=4
none of the above
f\left(x\right)=\left(x^2-x+3\right)^2 and c=225
12
What is a Tangent line?
a flat, two-dimensional surface that extends infinitely far.
a straight line that touches a function at only one point.
none of the above
a section of a line, connecting two points.
13
Find the slope of the tangent line at x = 1
1/4
8
1
-1/4
14
If the equation for the tangent line is y=6(x-4)+3, what is the equation for the normal line?
y=-6(x-4)+3
y=6(x-4)+3
y=\frac{1}{6} (x-4)+3
y=-\frac{1}{6} (x-4)+3
15
f(x) = 2x+3 and a= 1. Find the slope of the tangent line.
1/2
2
4
3
16
How many mathematicians are there in the world?
70 000
80 000
60 000
90 000

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