Why is 4X +5 a linear function Why is y=X2 a nonlinear function

1 answer:

4 0

y = 4x+5 is in the form y = mx+b which is slope intercept form. Anything in y = mx+b form is linear. It graphs out a straight line.

Contrast this with y = x^2 which is nonlinear because it graphs a curve that isnt a straight line. All quadratics like this graph out a parabola which resembles a bowl shaped curve.

You might be interested in

HELPPPPPPPPPPPP BRAINLY

AleksAgata [21]

Answer:

Step-by-step explanation:

6 0

1 year ago

Show that the sum of two concave functions is concave. Is the product of two concave functions also concave?

spayn [35]

Answer with explanation:

Let us assume that the 2 functions are:

1) f(x)

2) g(x)

Now by definition of concave function we have the first derivative of the function should be strictly decreasing thus for the above 2 function we conclude that

$\frac{d}{dx}\cdot f(x)$

Now the sum of the 2 functions is shown below

$y=f(x)+g(x)$

Diffrentiating both sides with respect to 'x' we get

$\frac{dy}{dx}=\frac{d}{dx}\cdot f(x)+\frac{d}{dx}\cdot g(x)\\\\$

Since each term in the right of the above equation is negative thus we conclude that their sum is also negative thus

$\frac{dy}{dx}$

Thus the sum of the 2 functions is also a concave function.

Part 2)

The product of the 2 functions is shown below

$h=f(x)\cdot g(x)$

Diffrentiating both sides with respect to 'x' we get

$h'=\frac{d}{dx}\cdot (f(x)\cdot g(x))\\\\h'=g(x)f'(x)+f(x)g'(x)$

Now we can see the sign of the terms on the right hand side depend on the signs of the function's themselves hence we remain inconclusive about the sign of the product as a whole. Thus the product can be concave or convex.

8 0

2 years ago

A ball is tossed up in the air at an initial rate of 50 ft/sec from 5 ft off the ground.

Fofino [41]

Answer with Step-by-step explanation:

Since we have given that

Initial velocity = 50 ft/sec = $v_0$