Question

If x is real then find the minimum value of 2x^2 -5x-3

Answer 1

Answer:

x = 3

Step-by-step explanation:

solution:-

Given:-

$2 {x}^{2} - 5x - 3 \\ \\ as \: this \: is \: in \: the \: form \: of \: \\ a {x}^{2} + bx + c \\ \\ \\ we \: can \: factorise \\ \\ 2 {x}^{2} - 5x - 3 \\ \\ 2 {x}^{2} - 6x + x - 3 \\ \\ make \: a \: pair \: n \: take \: common \\ \\ 2x(x - 3) + 1(x - 3) \\ \\ (x - 3)(2x + 1) \\ \\ now \\ \\ x - 3 = 0 \: \\ x = 3 \\ \\ 2x + 1 = 0 \\ 2x = - 1 \\ x = \frac{ - 1}{2}$

Answer 2

The minimum value of 2x²-5x-3 is -6.125.

• The given function is 2x²-5x-3.
• We have to find the minimum value of the function.
• To evaluate the minimum value of the function we use the first derivative test.

The first derivative test states that the slope of the tangent line at any point on the curve.

At the lowest point the slope of the equation will be equal to zero.

• Therefore evaluating the first derivative of the function with respect to x.

$\frac{dy}{dx} = \frac{d(2x^{2}-5x-3 )}{dx}$

$\frac{dy}{dx} = 4x - 5$

• The slope at this points must be equal to zero as it is the lowest point on the graph.

4x-5 = 0

x = 5/4 = 1.25

The value of x at which the function obtains the lowest point is x = 1.25.

• Now , obtaining the value of the function at x=1.25.

f(x) = 2x²-5x-3

f(x) = 2(1.25)²-5(1.25)-3

f(x) = 3.125-6.25-3

f(x) = -6.125

• This is the minimum value of the function.