The answers are as follow:
a) y'= -2x/y
b) y' = -4/y
<h3>Why do we use implicit differentiation?</h3>
The technique of implicit differentiation allows you to find the derivative of y with respect to x without having to solve the given equation for y.
Given:
x²y+4y=8
On differentiation
applying product rule
2xy+ x²y' = 0
2xy = - x²y'
2y = -xy'
y'= -2x/y
b) equation of the tangent line to the graph when x = 2.
y' = -4/y
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Answer:
x=-1/5
Step-by-step explanation:
2x2-x-1=0
-4x-x-1=0
-5×-1=0
-5×=1
×=-1/5
Step-by-step explanation:
Given -
Equations
- x + y = 8
- x - y = 3
To Find -
- which pair of coordinates satisfies both equation
Now,
adding both equation, we get -
x + y + x - y = 8 + 3
2x = 11
x = 11/2
<h3>x = 5.5</h3>
Now, substituting the value of x on x + y = 8, we get -
5.5 + y = 8
y = 8 - 5.5
<h3>y = 2.5</h3>
Hence,
(5.5, 2.5) pair of coordinates satisfies both equations.
Answer:
Because in the previous step we proved that two triangles were congruent, the answer is CPCTC.
Given:
The characteristic of an exponential parent function in the options.
To find:
Which is not a characteristic of an exponential parent function?
Solution:
The exponential parent function is:
Where, 
.
At 
,
It means the function passes through the point (0,1) but it does not passes through the origin. So, the statement in option A is true but the statement in option C is false.
The domain of the exponential parent function is all real numbers and the range is positive real numbers (y > 0). So, the statements in the options B and D are true.
Therefore, the correct option is C.
