Special Quiz 1
A.
1.
2.
3.
Tell whether the given statement is true or false. Write T if the statement is true and F otherwise.
A tangent line to a graph crosses the curve at one point.
A secant line to a graph crosses the curve at two points.
𝑦−𝑦
A line 𝑙 passing through distinct points (𝑥0 , 𝑦0 ) and (𝑥, 𝑦) has a slope of 𝑚𝑙 = 𝑥−𝑥0 .
0
4. Tangent line is a line that touches the circle at exactly one point and that is perpendicular to its radius.
5. The limit definition of the derivative is inherently indeterminate.
B. Determine the slope of the tangent line to the graph of each function at the given specified point. Then
given the equation of each tangent line in slope-intercept form.
1. 𝑓(𝑥) = 𝑥 3 − 3𝑥 2 + 2; 𝑃(3,2)
2. 𝑓(𝑥) = −
5
;
𝑥 2 +1
5
2
𝑃(−1, )
3. 𝑓(𝑥) = √5𝑥 + 5;
𝑃(4,5)
C. Determine the derivative of each function using the limit definition.
1. 𝐷𝑥 𝑦
if 𝑦 = −4𝑥 2 − 5𝑥 − 2
𝑥+1
2. 𝑓 ′ (𝑥)
if 𝑓(𝑥) = 𝑥−4
3. 𝑦′(1)
𝑦 = √𝑥 + 8 + 3𝑥
if
Special Quiz 1
A.
1.
2.
3.
Tell whether the given statement is true or false. Write T if the statement is true and F otherwise.
A tangent line to a graph crosses the curve at one point.
A secant line to a graph crosses the curve at two points.
𝑦−𝑦
A line 𝑙 passing through distinct points (𝑥0 , 𝑦0 ) and (𝑥, 𝑦) has a slope of 𝑚𝑙 = 𝑥−𝑥0 .
0
4. Tangent line is a line that touches the circle at exactly one point and that is perpendicular to its radius.
5. The limit definition of the derivative is inherently indeterminate.
B. Determine the slope of the tangent line to the graph of each function at the given specified point. Then
given the equation of each tangent line in slope-intercept form.
1. 𝑓(𝑥) = 𝑥 3 − 3𝑥 2 + 2; 𝑃(3,2)
5
5
2. 𝑓(𝑥) = − 𝑥 2 +1 ;
𝑃(−1, 2 )
3. 𝑓(𝑥) = √5𝑥 + 5;
𝑃(4,5)
C. Determine the derivative of each function using the limit definition.
1. 𝐷𝑥 𝑦
if 𝑦 = −4𝑥 2 − 5𝑥 − 2
𝑥+1
2. 𝑓 ′ (𝑥)
if 𝑓(𝑥) = 𝑥−4
3. 𝑦′(1)
if
𝑦 = √𝑥 + 8 + 3𝑥