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We have <br> `f(x)underset(0)overset(x)int (6t^2-24)dt on [1,3] ` is <br> `f(x)=6x2-24=6(x-2)(x+2)` <br> Signs of f(x) for differenet values of x are shown in <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/RDS_MATH_V02_C42_SLV_050_S01.png" width="80%"> <br> We observe that f(x) is decreasing in the interval (1,2) and inreasing in ther interval (2,3) Therefore , the least value of f(x) is given by <br> `f(2)=underset(0)overset(2)int (6t^2-24)dt =[2t^3-24t[_0^2`=-32 <br> and Greatest value of f(x)=Max {f(1),(f(x)} <br> We have <br> `f(1)=underset(0)overset(1)int (6t^2-24)dt =-20,f(3)=underset(0)overset(1)int(6t^2-24)dt =-18` <br> `therefore` Greatest value f(x)=-18 <br> Hence,required difference =-18-(-32)=14 **meaning of function**

**Modulus; signum; greatest integer and fractional part function**

**representation of function**

**Physical interpretation**

**Domain codomain and range of function**

**Graph of function: Vertical line test**

**Identity function**

**Explain Constant function with graph**

**Modulus function and properties**

**Greatest integer function and properties**